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Simplifying (x + 4)(x + -6) = (2x + 3)(x + -6) Reorder the terms: (4 + x)(x + -6) = (2x + 3)(x + -6) Reorder the terms: (4 + x)(-6 + x) = (2x + 3)(x + -6) Multiply (4 + x) * (-6 + x) (4(-6 + x) + x(-6 + x)) = (2x + 3)(x + -6) ((-6 * 4 + x * 4) + x(-6 + x)) = (2x + 3)(x + -6) ((-24 + 4x) + x(-6 + x)) = (2x + 3)(x + -6) (-24 + 4x + (-6 * x + x * x)) = (2x + 3)(x + -6) (-24 + 4x + (-6x + x2)) = (2x + 3)(x + -6) Combine like terms: 4x + -6x = -2x (-24 + -2x + x2) = (2x + 3)(x + -6) Reorder the terms: -24 + -2x + x2 = (3 + 2x)(x + -6) Reorder the terms: -24 + -2x + x2 = (3 + 2x)(-6 + x) Multiply (3 + 2x) * (-6 + x) -24 + -2x + x2 = (3(-6 + x) + 2x * (-6 + x)) -24 + -2x + x2 = ((-6 * 3 + x * 3) + 2x * (-6 + x)) -24 + -2x + x2 = ((-18 + 3x) + 2x * (-6 + x)) -24 + -2x + x2 = (-18 + 3x + (-6 * 2x + x * 2x)) -24 + -2x + x2 = (-18 + 3x + (-12x + 2x2)) Combine like terms: 3x + -12x = -9x -24 + -2x + x2 = (-18 + -9x + 2x2) Solving -24 + -2x + x2 = -18 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: -24 + 18 + -2x + 9x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2 Combine like terms: -24 + 18 = -6 -6 + -2x + 9x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2 Combine like terms: -2x + 9x = 7x -6 + 7x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -6 + 7x + -1x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2 Reorder the terms: -6 + 7x + -1x2 = -18 + 18 + -9x + 9x + 2x2 + -2x2 Combine like terms: -18 + 18 = 0 -6 + 7x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2 -6 + 7x + -1x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 -6 + 7x + -1x2 = 0 + 2x2 + -2x2 -6 + 7x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + 7x + -1x2 = 0 Factor a trinomial. (-6 + x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {6, 1}
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