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Simplifying 2x(x + -3) + -2(x + 3)(x + -3) = (x + -12)(x + 3) Reorder the terms: 2x(-3 + x) + -2(x + 3)(x + -3) = (x + -12)(x + 3) (-3 * 2x + x * 2x) + -2(x + 3)(x + -3) = (x + -12)(x + 3) (-6x + 2x2) + -2(x + 3)(x + -3) = (x + -12)(x + 3) Reorder the terms: -6x + 2x2 + -2(3 + x)(x + -3) = (x + -12)(x + 3) Reorder the terms: -6x + 2x2 + -2(3 + x)(-3 + x) = (x + -12)(x + 3) Multiply (3 + x) * (-3 + x) -6x + 2x2 + -2(3(-3 + x) + x(-3 + x)) = (x + -12)(x + 3) -6x + 2x2 + -2((-3 * 3 + x * 3) + x(-3 + x)) = (x + -12)(x + 3) -6x + 2x2 + -2((-9 + 3x) + x(-3 + x)) = (x + -12)(x + 3) -6x + 2x2 + -2(-9 + 3x + (-3 * x + x * x)) = (x + -12)(x + 3) -6x + 2x2 + -2(-9 + 3x + (-3x + x2)) = (x + -12)(x + 3) Combine like terms: 3x + -3x = 0 -6x + 2x2 + -2(-9 + 0 + x2) = (x + -12)(x + 3) -6x + 2x2 + -2(-9 + x2) = (x + -12)(x + 3) -6x + 2x2 + (-9 * -2 + x2 * -2) = (x + -12)(x + 3) -6x + 2x2 + (18 + -2x2) = (x + -12)(x + 3) Reorder the terms: 18 + -6x + 2x2 + -2x2 = (x + -12)(x + 3) Combine like terms: 2x2 + -2x2 = 0 18 + -6x + 0 = (x + -12)(x + 3) 18 + -6x = (x + -12)(x + 3) Reorder the terms: 18 + -6x = (-12 + x)(x + 3) Reorder the terms: 18 + -6x = (-12 + x)(3 + x) Multiply (-12 + x) * (3 + x) 18 + -6x = (-12(3 + x) + x(3 + x)) 18 + -6x = ((3 * -12 + x * -12) + x(3 + x)) 18 + -6x = ((-36 + -12x) + x(3 + x)) 18 + -6x = (-36 + -12x + (3 * x + x * x)) 18 + -6x = (-36 + -12x + (3x + x2)) Combine like terms: -12x + 3x = -9x 18 + -6x = (-36 + -9x + x2) Solving 18 + -6x = -36 + -9x + x2 Solving for variable 'x'. Reorder the terms: 18 + 36 + -6x + 9x + -1x2 = -36 + -9x + x2 + 36 + 9x + -1x2 Combine like terms: 18 + 36 = 54 54 + -6x + 9x + -1x2 = -36 + -9x + x2 + 36 + 9x + -1x2 Combine like terms: -6x + 9x = 3x 54 + 3x + -1x2 = -36 + -9x + x2 + 36 + 9x + -1x2 Reorder the terms: 54 + 3x + -1x2 = -36 + 36 + -9x + 9x + x2 + -1x2 Combine like terms: -36 + 36 = 0 54 + 3x + -1x2 = 0 + -9x + 9x + x2 + -1x2 54 + 3x + -1x2 = -9x + 9x + x2 + -1x2 Combine like terms: -9x + 9x = 0 54 + 3x + -1x2 = 0 + x2 + -1x2 54 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54 + 3x + -1x2 = 0 Factor a trinomial. (9 + -1x)(6 + x) = 0Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {9, -6}
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