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Simplifying (x + 1)(x + -6) = (2x + 3)(x + -6) Reorder the terms: (1 + x)(x + -6) = (2x + 3)(x + -6) Reorder the terms: (1 + x)(-6 + x) = (2x + 3)(x + -6) Multiply (1 + x) * (-6 + x) (1(-6 + x) + x(-6 + x)) = (2x + 3)(x + -6) ((-6 * 1 + x * 1) + x(-6 + x)) = (2x + 3)(x + -6) ((-6 + 1x) + x(-6 + x)) = (2x + 3)(x + -6) (-6 + 1x + (-6 * x + x * x)) = (2x + 3)(x + -6) (-6 + 1x + (-6x + x2)) = (2x + 3)(x + -6) Combine like terms: 1x + -6x = -5x (-6 + -5x + x2) = (2x + 3)(x + -6) Reorder the terms: -6 + -5x + x2 = (3 + 2x)(x + -6) Reorder the terms: -6 + -5x + x2 = (3 + 2x)(-6 + x) Multiply (3 + 2x) * (-6 + x) -6 + -5x + x2 = (3(-6 + x) + 2x * (-6 + x)) -6 + -5x + x2 = ((-6 * 3 + x * 3) + 2x * (-6 + x)) -6 + -5x + x2 = ((-18 + 3x) + 2x * (-6 + x)) -6 + -5x + x2 = (-18 + 3x + (-6 * 2x + x * 2x)) -6 + -5x + x2 = (-18 + 3x + (-12x + 2x2)) Combine like terms: 3x + -12x = -9x -6 + -5x + x2 = (-18 + -9x + 2x2) Solving -6 + -5x + x2 = -18 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: -6 + 18 + -5x + 9x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2 Combine like terms: -6 + 18 = 12 12 + -5x + 9x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2 Combine like terms: -5x + 9x = 4x 12 + 4x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2 Combine like terms: x2 + -2x2 = -1x2 12 + 4x + -1x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2 Reorder the terms: 12 + 4x + -1x2 = -18 + 18 + -9x + 9x + 2x2 + -2x2 Combine like terms: -18 + 18 = 0 12 + 4x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2 12 + 4x + -1x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 12 + 4x + -1x2 = 0 + 2x2 + -2x2 12 + 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12 + 4x + -1x2 = 0 Factor a trinomial. (6 + -1x)(2 + x) = 0Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {6, -2}
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