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Simplifying (x2 + -1)(x + -2) = 14x + 2 Reorder the terms: (-1 + x2)(x + -2) = 14x + 2 Reorder the terms: (-1 + x2)(-2 + x) = 14x + 2 Multiply (-1 + x2) * (-2 + x) (-1(-2 + x) + x2(-2 + x)) = 14x + 2 ((-2 * -1 + x * -1) + x2(-2 + x)) = 14x + 2 ((2 + -1x) + x2(-2 + x)) = 14x + 2 (2 + -1x + (-2 * x2 + x * x2)) = 14x + 2 (2 + -1x + (-2x2 + x3)) = 14x + 2 (2 + -1x + -2x2 + x3) = 14x + 2 Reorder the terms: 2 + -1x + -2x2 + x3 = 2 + 14x Add '-2' to each side of the equation. 2 + -1x + -2x2 + -2 + x3 = 2 + -2 + 14x Reorder the terms: 2 + -2 + -1x + -2x2 + x3 = 2 + -2 + 14x Combine like terms: 2 + -2 = 0 0 + -1x + -2x2 + x3 = 2 + -2 + 14x -1x + -2x2 + x3 = 2 + -2 + 14x Combine like terms: 2 + -2 = 0 -1x + -2x2 + x3 = 0 + 14x -1x + -2x2 + x3 = 14x Solving -1x + -2x2 + x3 = 14x Solving for variable 'x'. Reorder the terms: -1x + -14x + -2x2 + x3 = 14x + -14x Combine like terms: -1x + -14x = -15x -15x + -2x2 + x3 = 14x + -14x Combine like terms: 14x + -14x = 0 -15x + -2x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-15 + -2x + x2) = 0 Factor a trinomial. x((-3 + -1x)(5 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = -3Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, -3, 5}
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