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