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Simplifying 6(x + -5)(x + -2) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) Reorder the terms: 6(-5 + x)(x + -2) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) Reorder the terms: 6(-5 + x)(-2 + x) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) Multiply (-5 + x) * (-2 + x) 6(-5(-2 + x) + x(-2 + x)) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) 6((-2 * -5 + x * -5) + x(-2 + x)) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) 6((10 + -5x) + x(-2 + x)) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) 6(10 + -5x + (-2 * x + x * x)) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) 6(10 + -5x + (-2x + x2)) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) Combine like terms: -5x + -2x = -7x 6(10 + -7x + x2) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) (10 * 6 + -7x * 6 + x2 * 6) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) (60 + -42x + 6x2) + -2(x + -3)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) Reorder the terms: 60 + -42x + 6x2 + -2(-3 + x)(x + -4)(x + -2) = 2x(x + -3)(x + -4)(x + -5) Reorder the terms: 60 + -42x + 6x2 + -2(-3 + x)(-4 + x)(x + -2) = 2x(x + -3)(x + -4)(x + -5) Reorder the terms: 60 + -42x + 6x2 + -2(-3 + x)(-4 + x)(-2 + x) = 2x(x + -3)(x + -4)(x + -5) Multiply (-3 + x) * (-4 + x) 60 + -42x + 6x2 + -2(-3(-4 + x) + x(-4 + x))(-2 + x) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2((-4 * -3 + x * -3) + x(-4 + x))(-2 + x) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2((12 + -3x) + x(-4 + x))(-2 + x) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2(12 + -3x + (-4 * x + x * x))(-2 + x) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2(12 + -3x + (-4x + x2))(-2 + x) = 2x(x + -3)(x + -4)(x + -5) Combine like terms: -3x + -4x = -7x 60 + -42x + 6x2 + -2(12 + -7x + x2)(-2 + x) = 2x(x + -3)(x + -4)(x + -5) Multiply (12 + -7x + x2) * (-2 + x) 60 + -42x + 6x2 + -2(12(-2 + x) + -7x * (-2 + x) + x2(-2 + x)) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2((-2 * 12 + x * 12) + -7x * (-2 + x) + x2(-2 + x)) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2((-24 + 12x) + -7x * (-2 + x) + x2(-2 + x)) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2(-24 + 12x + (-2 * -7x + x * -7x) + x2(-2 + x)) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2(-24 + 12x + (14x + -7x2) + x2(-2 + x)) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2(-24 + 12x + 14x + -7x2 + (-2 * x2 + x * x2)) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + -2(-24 + 12x + 14x + -7x2 + (-2x2 + x3)) = 2x(x + -3)(x + -4)(x + -5) Combine like terms: 12x + 14x = 26x 60 + -42x + 6x2 + -2(-24 + 26x + -7x2 + -2x2 + x3) = 2x(x + -3)(x + -4)(x + -5) Combine like terms: -7x2 + -2x2 = -9x2 60 + -42x + 6x2 + -2(-24 + 26x + -9x2 + x3) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + (-24 * -2 + 26x * -2 + -9x2 * -2 + x3 * -2) = 2x(x + -3)(x + -4)(x + -5) 60 + -42x + 6x2 + (48 + -52x + 18x2 + -2x3) = 2x(x + -3)(x + -4)(x + -5) Reorder the terms: 60 + 48 + -42x + -52x + 6x2 + 18x2 + -2x3 = 2x(x + -3)(x + -4)(x + -5) Combine like terms: 60 + 48 = 108 108 + -42x + -52x + 6x2 + 18x2 + -2x3 = 2x(x + -3)(x + -4)(x + -5) Combine like terms: -42x + -52x = -94x 108 + -94x + 6x2 + 18x2 + -2x3 = 2x(x + -3)(x + -4)(x + -5) Combine like terms: 6x2 + 18x2 = 24x2 108 + -94x + 24x2 + -2x3 = 2x(x + -3)(x + -4)(x + -5) Reorder the terms: 108 + -94x + 24x2 + -2x3 = 2x(-3 + x)(x + -4)(x + -5) Reorder the terms: 108 + -94x + 24x2 + -2x3 = 2x(-3 + x)(-4 + x)(x + -5) Reorder the terms: 108 + -94x + 24x2 + -2x3 = 2x(-3 + x)(-4 + x)(-5 + x) Multiply (-3 + x) * (-4 + x) 108 + -94x + 24x2 + -2x3 = 2x(-3(-4 + x) + x(-4 + x))(-5 + x) 108 + -94x + 24x2 + -2x3 = 2x((-4 * -3 + x * -3) + x(-4 + x))(-5 + x) 108 + -94x + 24x2 + -2x3 = 2x((12 + -3x) + x(-4 + x))(-5 + x) 108 + -94x + 24x2 + -2x3 = 2x(12 + -3x + (-4 * x + x * x))(-5 + x) 108 + -94x + 24x2 + -2x3 = 2x(12 + -3x + (-4x + x2))(-5 + x) Combine like terms: -3x + -4x = -7x 108 + -94x + 24x2 + -2x3 = 2x(12 + -7x + x2)(-5 + x) Multiply (12 + -7x + x2) * (-5 + x) 108 + -94x + 24x2 + -2x3 = 2x(12(-5 + x) + -7x * (-5 + x) + x2(-5 + x)) 108 + -94x + 24x2 + -2x3 = 2x((-5 * 12 + x * 12) + -7x * (-5 + x) + x2(-5 + x)) 108 + -94x + 24x2 + -2x3 = 2x((-60 + 12x) + -7x * (-5 + x) + x2(-5 + x)) 108 + -94x + 24x2 + -2x3 = 2x(-60 + 12x + (-5 * -7x + x * -7x) + x2(-5 + x)) 108 + -94x + 24x2 + -2x3 = 2x(-60 + 12x + (35x + -7x2) + x2(-5 + x)) 108 + -94x + 24x2 + -2x3 = 2x(-60 + 12x + 35x + -7x2 + (-5 * x2 + x * x2)) 108 + -94x + 24x2 + -2x3 = 2x(-60 + 12x + 35x + -7x2 + (-5x2 + x3)) Combine like terms: 12x + 35x = 47x 108 + -94x + 24x2 + -2x3 = 2x(-60 + 47x + -7x2 + -5x2 + x3) Combine like terms: -7x2 + -5x2 = -12x2 108 + -94x + 24x2 + -2x3 = 2x(-60 + 47x + -12x2 + x3) 108 + -94x + 24x2 + -2x3 = (-60 * 2x + 47x * 2x + -12x2 * 2x + x3 * 2x) 108 + -94x + 24x2 + -2x3 = (-120x + 94x2 + -24x3 + 2x4) Solving 108 + -94x + 24x2 + -2x3 = -120x + 94x2 + -24x3 + 2x4 Solving for variable 'x'. Reorder the terms: 108 + -94x + 120x + 24x2 + -94x2 + -2x3 + 24x3 + -2x4 = -120x + 94x2 + -24x3 + 2x4 + 120x + -94x2 + 24x3 + -2x4 Combine like terms: -94x + 120x = 26x 108 + 26x + 24x2 + -94x2 + -2x3 + 24x3 + -2x4 = -120x + 94x2 + -24x3 + 2x4 + 120x + -94x2 + 24x3 + -2x4 Combine like terms: 24x2 + -94x2 = -70x2 108 + 26x + -70x2 + -2x3 + 24x3 + -2x4 = -120x + 94x2 + -24x3 + 2x4 + 120x + -94x2 + 24x3 + -2x4 Combine like terms: -2x3 + 24x3 = 22x3 108 + 26x + -70x2 + 22x3 + -2x4 = -120x + 94x2 + -24x3 + 2x4 + 120x + -94x2 + 24x3 + -2x4 Reorder the terms: 108 + 26x + -70x2 + 22x3 + -2x4 = -120x + 120x + 94x2 + -94x2 + -24x3 + 24x3 + 2x4 + -2x4 Combine like terms: -120x + 120x = 0 108 + 26x + -70x2 + 22x3 + -2x4 = 0 + 94x2 + -94x2 + -24x3 + 24x3 + 2x4 + -2x4 108 + 26x + -70x2 + 22x3 + -2x4 = 94x2 + -94x2 + -24x3 + 24x3 + 2x4 + -2x4 Combine like terms: 94x2 + -94x2 = 0 108 + 26x + -70x2 + 22x3 + -2x4 = 0 + -24x3 + 24x3 + 2x4 + -2x4 108 + 26x + -70x2 + 22x3 + -2x4 = -24x3 + 24x3 + 2x4 + -2x4 Combine like terms: -24x3 + 24x3 = 0 108 + 26x + -70x2 + 22x3 + -2x4 = 0 + 2x4 + -2x4 108 + 26x + -70x2 + 22x3 + -2x4 = 2x4 + -2x4 Combine like terms: 2x4 + -2x4 = 0 108 + 26x + -70x2 + 22x3 + -2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(54 + 13x + -35x2 + 11x3 + -1x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(54 + 13x + -35x2 + 11x3 + -1x4)' equal to zero and attempt to solve: Simplifying 54 + 13x + -35x2 + 11x3 + -1x4 = 0 Solving 54 + 13x + -35x2 + 11x3 + -1x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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