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Simplifying 15(x + -2)(x + -4) + -8(x + -3)(x + -5) = 0 Reorder the terms: 15(-2 + x)(x + -4) + -8(x + -3)(x + -5) = 0 Reorder the terms: 15(-2 + x)(-4 + x) + -8(x + -3)(x + -5) = 0 Multiply (-2 + x) * (-4 + x) 15(-2(-4 + x) + x(-4 + x)) + -8(x + -3)(x + -5) = 0 15((-4 * -2 + x * -2) + x(-4 + x)) + -8(x + -3)(x + -5) = 0 15((8 + -2x) + x(-4 + x)) + -8(x + -3)(x + -5) = 0 15(8 + -2x + (-4 * x + x * x)) + -8(x + -3)(x + -5) = 0 15(8 + -2x + (-4x + x2)) + -8(x + -3)(x + -5) = 0 Combine like terms: -2x + -4x = -6x 15(8 + -6x + x2) + -8(x + -3)(x + -5) = 0 (8 * 15 + -6x * 15 + x2 * 15) + -8(x + -3)(x + -5) = 0 (120 + -90x + 15x2) + -8(x + -3)(x + -5) = 0 Reorder the terms: 120 + -90x + 15x2 + -8(-3 + x)(x + -5) = 0 Reorder the terms: 120 + -90x + 15x2 + -8(-3 + x)(-5 + x) = 0 Multiply (-3 + x) * (-5 + x) 120 + -90x + 15x2 + -8(-3(-5 + x) + x(-5 + x)) = 0 120 + -90x + 15x2 + -8((-5 * -3 + x * -3) + x(-5 + x)) = 0 120 + -90x + 15x2 + -8((15 + -3x) + x(-5 + x)) = 0 120 + -90x + 15x2 + -8(15 + -3x + (-5 * x + x * x)) = 0 120 + -90x + 15x2 + -8(15 + -3x + (-5x + x2)) = 0 Combine like terms: -3x + -5x = -8x 120 + -90x + 15x2 + -8(15 + -8x + x2) = 0 120 + -90x + 15x2 + (15 * -8 + -8x * -8 + x2 * -8) = 0 120 + -90x + 15x2 + (-120 + 64x + -8x2) = 0 Reorder the terms: 120 + -120 + -90x + 64x + 15x2 + -8x2 = 0 Combine like terms: 120 + -120 = 0 0 + -90x + 64x + 15x2 + -8x2 = 0 -90x + 64x + 15x2 + -8x2 = 0 Combine like terms: -90x + 64x = -26x -26x + 15x2 + -8x2 = 0 Combine like terms: 15x2 + -8x2 = 7x2 -26x + 7x2 = 0 Solving -26x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-26 + 7x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-26 + 7x)' equal to zero and attempt to solve: Simplifying -26 + 7x = 0 Solving -26 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + 7x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 7x = 0 + 26 7x = 0 + 26 Combine like terms: 0 + 26 = 26 7x = 26 Divide each side by '7'. x = 3.714285714 Simplifying x = 3.714285714Solution
x = {0, 3.714285714}
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