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Simplifying (x + 6)(x + -2) = (2x + 1)(x + -2) Reorder the terms: (6 + x)(x + -2) = (2x + 1)(x + -2) Reorder the terms: (6 + x)(-2 + x) = (2x + 1)(x + -2) Multiply (6 + x) * (-2 + x) (6(-2 + x) + x(-2 + x)) = (2x + 1)(x + -2) ((-2 * 6 + x * 6) + x(-2 + x)) = (2x + 1)(x + -2) ((-12 + 6x) + x(-2 + x)) = (2x + 1)(x + -2) (-12 + 6x + (-2 * x + x * x)) = (2x + 1)(x + -2) (-12 + 6x + (-2x + x2)) = (2x + 1)(x + -2) Combine like terms: 6x + -2x = 4x (-12 + 4x + x2) = (2x + 1)(x + -2) Reorder the terms: -12 + 4x + x2 = (1 + 2x)(x + -2) Reorder the terms: -12 + 4x + x2 = (1 + 2x)(-2 + x) Multiply (1 + 2x) * (-2 + x) -12 + 4x + x2 = (1(-2 + x) + 2x * (-2 + x)) -12 + 4x + x2 = ((-2 * 1 + x * 1) + 2x * (-2 + x)) -12 + 4x + x2 = ((-2 + 1x) + 2x * (-2 + x)) -12 + 4x + x2 = (-2 + 1x + (-2 * 2x + x * 2x)) -12 + 4x + x2 = (-2 + 1x + (-4x + 2x2)) Combine like terms: 1x + -4x = -3x -12 + 4x + x2 = (-2 + -3x + 2x2) Solving -12 + 4x + x2 = -2 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: -12 + 2 + 4x + 3x + x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2 Combine like terms: -12 + 2 = -10 -10 + 4x + 3x + x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2 Combine like terms: 4x + 3x = 7x -10 + 7x + x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -10 + 7x + -1x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2 Reorder the terms: -10 + 7x + -1x2 = -2 + 2 + -3x + 3x + 2x2 + -2x2 Combine like terms: -2 + 2 = 0 -10 + 7x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2 -10 + 7x + -1x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 -10 + 7x + -1x2 = 0 + 2x2 + -2x2 -10 + 7x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -10 + 7x + -1x2 = 0 Factor a trinomial. (-5 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 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 = {5, 2}
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