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Simplifying 2(2x + -5)(3x + 4) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 Reorder the terms: 2(-5 + 2x)(3x + 4) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 Reorder the terms: 2(-5 + 2x)(4 + 3x) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 Multiply (-5 + 2x) * (4 + 3x) 2(-5(4 + 3x) + 2x * (4 + 3x)) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 2((4 * -5 + 3x * -5) + 2x * (4 + 3x)) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 2((-20 + -15x) + 2x * (4 + 3x)) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 2(-20 + -15x + (4 * 2x + 3x * 2x)) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 2(-20 + -15x + (8x + 6x2)) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 Combine like terms: -15x + 8x = -7x 2(-20 + -7x + 6x2) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 (-20 * 2 + -7x * 2 + 6x2 * 2) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 (-40 + -14x + 12x2) + -1(2 + -3x)(2 + -3x) = (x + 3)(x + 3) + 67 Multiply (2 + -3x) * (2 + -3x) -40 + -14x + 12x2 + -1(2(2 + -3x) + -3x * (2 + -3x)) = (x + 3)(x + 3) + 67 -40 + -14x + 12x2 + -1((2 * 2 + -3x * 2) + -3x * (2 + -3x)) = (x + 3)(x + 3) + 67 -40 + -14x + 12x2 + -1((4 + -6x) + -3x * (2 + -3x)) = (x + 3)(x + 3) + 67 -40 + -14x + 12x2 + -1(4 + -6x + (2 * -3x + -3x * -3x)) = (x + 3)(x + 3) + 67 -40 + -14x + 12x2 + -1(4 + -6x + (-6x + 9x2)) = (x + 3)(x + 3) + 67 Combine like terms: -6x + -6x = -12x -40 + -14x + 12x2 + -1(4 + -12x + 9x2) = (x + 3)(x + 3) + 67 -40 + -14x + 12x2 + (4 * -1 + -12x * -1 + 9x2 * -1) = (x + 3)(x + 3) + 67 -40 + -14x + 12x2 + (-4 + 12x + -9x2) = (x + 3)(x + 3) + 67 Reorder the terms: -40 + -4 + -14x + 12x + 12x2 + -9x2 = (x + 3)(x + 3) + 67 Combine like terms: -40 + -4 = -44 -44 + -14x + 12x + 12x2 + -9x2 = (x + 3)(x + 3) + 67 Combine like terms: -14x + 12x = -2x -44 + -2x + 12x2 + -9x2 = (x + 3)(x + 3) + 67 Combine like terms: 12x2 + -9x2 = 3x2 -44 + -2x + 3x2 = (x + 3)(x + 3) + 67 Reorder the terms: -44 + -2x + 3x2 = (3 + x)(x + 3) + 67 Reorder the terms: -44 + -2x + 3x2 = (3 + x)(3 + x) + 67 Multiply (3 + x) * (3 + x) -44 + -2x + 3x2 = (3(3 + x) + x(3 + x)) + 67 -44 + -2x + 3x2 = ((3 * 3 + x * 3) + x(3 + x)) + 67 -44 + -2x + 3x2 = ((9 + 3x) + x(3 + x)) + 67 -44 + -2x + 3x2 = (9 + 3x + (3 * x + x * x)) + 67 -44 + -2x + 3x2 = (9 + 3x + (3x + x2)) + 67 Combine like terms: 3x + 3x = 6x -44 + -2x + 3x2 = (9 + 6x + x2) + 67 Reorder the terms: -44 + -2x + 3x2 = 9 + 67 + 6x + x2 Combine like terms: 9 + 67 = 76 -44 + -2x + 3x2 = 76 + 6x + x2 Solving -44 + -2x + 3x2 = 76 + 6x + x2 Solving for variable 'x'. Reorder the terms: -44 + -76 + -2x + -6x + 3x2 + -1x2 = 76 + 6x + x2 + -76 + -6x + -1x2 Combine like terms: -44 + -76 = -120 -120 + -2x + -6x + 3x2 + -1x2 = 76 + 6x + x2 + -76 + -6x + -1x2 Combine like terms: -2x + -6x = -8x -120 + -8x + 3x2 + -1x2 = 76 + 6x + x2 + -76 + -6x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -120 + -8x + 2x2 = 76 + 6x + x2 + -76 + -6x + -1x2 Reorder the terms: -120 + -8x + 2x2 = 76 + -76 + 6x + -6x + x2 + -1x2 Combine like terms: 76 + -76 = 0 -120 + -8x + 2x2 = 0 + 6x + -6x + x2 + -1x2 -120 + -8x + 2x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -120 + -8x + 2x2 = 0 + x2 + -1x2 -120 + -8x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -120 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + -4x + x2) = 0 Factor a trinomial. 2((-6 + -1x)(10 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-6, 10}
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