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Simplifying (x + -3)(5 + 2x) + -1(x + -3)(x + -6) = 0 Reorder the terms: (-3 + x)(5 + 2x) + -1(x + -3)(x + -6) = 0 Multiply (-3 + x) * (5 + 2x) (-3(5 + 2x) + x(5 + 2x)) + -1(x + -3)(x + -6) = 0 ((5 * -3 + 2x * -3) + x(5 + 2x)) + -1(x + -3)(x + -6) = 0 ((-15 + -6x) + x(5 + 2x)) + -1(x + -3)(x + -6) = 0 (-15 + -6x + (5 * x + 2x * x)) + -1(x + -3)(x + -6) = 0 (-15 + -6x + (5x + 2x2)) + -1(x + -3)(x + -6) = 0 Combine like terms: -6x + 5x = -1x (-15 + -1x + 2x2) + -1(x + -3)(x + -6) = 0 Reorder the terms: -15 + -1x + 2x2 + -1(-3 + x)(x + -6) = 0 Reorder the terms: -15 + -1x + 2x2 + -1(-3 + x)(-6 + x) = 0 Multiply (-3 + x) * (-6 + x) -15 + -1x + 2x2 + -1(-3(-6 + x) + x(-6 + x)) = 0 -15 + -1x + 2x2 + -1((-6 * -3 + x * -3) + x(-6 + x)) = 0 -15 + -1x + 2x2 + -1((18 + -3x) + x(-6 + x)) = 0 -15 + -1x + 2x2 + -1(18 + -3x + (-6 * x + x * x)) = 0 -15 + -1x + 2x2 + -1(18 + -3x + (-6x + x2)) = 0 Combine like terms: -3x + -6x = -9x -15 + -1x + 2x2 + -1(18 + -9x + x2) = 0 -15 + -1x + 2x2 + (18 * -1 + -9x * -1 + x2 * -1) = 0 -15 + -1x + 2x2 + (-18 + 9x + -1x2) = 0 Reorder the terms: -15 + -18 + -1x + 9x + 2x2 + -1x2 = 0 Combine like terms: -15 + -18 = -33 -33 + -1x + 9x + 2x2 + -1x2 = 0 Combine like terms: -1x + 9x = 8x -33 + 8x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -33 + 8x + 1x2 = 0 Solving -33 + 8x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-11 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-11, 3}
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