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Simplifying (x + 4)(x + -6) = (2x + 1)(x + -6) Reorder the terms: (4 + x)(x + -6) = (2x + 1)(x + -6) Reorder the terms: (4 + x)(-6 + x) = (2x + 1)(x + -6) Multiply (4 + x) * (-6 + x) (4(-6 + x) + x(-6 + x)) = (2x + 1)(x + -6) ((-6 * 4 + x * 4) + x(-6 + x)) = (2x + 1)(x + -6) ((-24 + 4x) + x(-6 + x)) = (2x + 1)(x + -6) (-24 + 4x + (-6 * x + x * x)) = (2x + 1)(x + -6) (-24 + 4x + (-6x + x2)) = (2x + 1)(x + -6) Combine like terms: 4x + -6x = -2x (-24 + -2x + x2) = (2x + 1)(x + -6) Reorder the terms: -24 + -2x + x2 = (1 + 2x)(x + -6) Reorder the terms: -24 + -2x + x2 = (1 + 2x)(-6 + x) Multiply (1 + 2x) * (-6 + x) -24 + -2x + x2 = (1(-6 + x) + 2x * (-6 + x)) -24 + -2x + x2 = ((-6 * 1 + x * 1) + 2x * (-6 + x)) -24 + -2x + x2 = ((-6 + 1x) + 2x * (-6 + x)) -24 + -2x + x2 = (-6 + 1x + (-6 * 2x + x * 2x)) -24 + -2x + x2 = (-6 + 1x + (-12x + 2x2)) Combine like terms: 1x + -12x = -11x -24 + -2x + x2 = (-6 + -11x + 2x2) Solving -24 + -2x + x2 = -6 + -11x + 2x2 Solving for variable 'x'. Reorder the terms: -24 + 6 + -2x + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: -24 + 6 = -18 -18 + -2x + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: -2x + 11x = 9x -18 + 9x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -18 + 9x + -1x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Reorder the terms: -18 + 9x + -1x2 = -6 + 6 + -11x + 11x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 -18 + 9x + -1x2 = 0 + -11x + 11x + 2x2 + -2x2 -18 + 9x + -1x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 -18 + 9x + -1x2 = 0 + 2x2 + -2x2 -18 + 9x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -18 + 9x + -1x2 = 0 Factor a trinomial. (-6 + x)(3 + -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 '(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 = {6, 3}
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