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Simplifying (x + 3)(x + -6) = (2x + 1)(x + -6) Reorder the terms: (3 + x)(x + -6) = (2x + 1)(x + -6) Reorder the terms: (3 + x)(-6 + x) = (2x + 1)(x + -6) Multiply (3 + x) * (-6 + x) (3(-6 + x) + x(-6 + x)) = (2x + 1)(x + -6) ((-6 * 3 + x * 3) + x(-6 + x)) = (2x + 1)(x + -6) ((-18 + 3x) + x(-6 + x)) = (2x + 1)(x + -6) (-18 + 3x + (-6 * x + x * x)) = (2x + 1)(x + -6) (-18 + 3x + (-6x + x2)) = (2x + 1)(x + -6) Combine like terms: 3x + -6x = -3x (-18 + -3x + x2) = (2x + 1)(x + -6) Reorder the terms: -18 + -3x + x2 = (1 + 2x)(x + -6) Reorder the terms: -18 + -3x + x2 = (1 + 2x)(-6 + x) Multiply (1 + 2x) * (-6 + x) -18 + -3x + x2 = (1(-6 + x) + 2x * (-6 + x)) -18 + -3x + x2 = ((-6 * 1 + x * 1) + 2x * (-6 + x)) -18 + -3x + x2 = ((-6 + 1x) + 2x * (-6 + x)) -18 + -3x + x2 = (-6 + 1x + (-6 * 2x + x * 2x)) -18 + -3x + x2 = (-6 + 1x + (-12x + 2x2)) Combine like terms: 1x + -12x = -11x -18 + -3x + x2 = (-6 + -11x + 2x2) Solving -18 + -3x + x2 = -6 + -11x + 2x2 Solving for variable 'x'. Reorder the terms: -18 + 6 + -3x + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: -18 + 6 = -12 -12 + -3x + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: -3x + 11x = 8x -12 + 8x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -12 + 8x + -1x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Reorder the terms: -12 + 8x + -1x2 = -6 + 6 + -11x + 11x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 -12 + 8x + -1x2 = 0 + -11x + 11x + 2x2 + -2x2 -12 + 8x + -1x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 -12 + 8x + -1x2 = 0 + 2x2 + -2x2 -12 + 8x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 8x + -1x2 = 0 Factor a trinomial. (-6 + x)(2 + -1x) = 0Subproblem 1
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 = 6Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {6, 2}
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