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Simplifying 2x(x + 4) = (x + 6)(x + 4) Reorder the terms: 2x(4 + x) = (x + 6)(x + 4) (4 * 2x + x * 2x) = (x + 6)(x + 4) (8x + 2x2) = (x + 6)(x + 4) Reorder the terms: 8x + 2x2 = (6 + x)(x + 4) Reorder the terms: 8x + 2x2 = (6 + x)(4 + x) Multiply (6 + x) * (4 + x) 8x + 2x2 = (6(4 + x) + x(4 + x)) 8x + 2x2 = ((4 * 6 + x * 6) + x(4 + x)) 8x + 2x2 = ((24 + 6x) + x(4 + x)) 8x + 2x2 = (24 + 6x + (4 * x + x * x)) 8x + 2x2 = (24 + 6x + (4x + x2)) Combine like terms: 6x + 4x = 10x 8x + 2x2 = (24 + 10x + x2) Solving 8x + 2x2 = 24 + 10x + x2 Solving for variable 'x'. Reorder the terms: -24 + 8x + -10x + 2x2 + -1x2 = 24 + 10x + x2 + -24 + -10x + -1x2 Combine like terms: 8x + -10x = -2x -24 + -2x + 2x2 + -1x2 = 24 + 10x + x2 + -24 + -10x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -24 + -2x + 1x2 = 24 + 10x + x2 + -24 + -10x + -1x2 Reorder the terms: -24 + -2x + 1x2 = 24 + -24 + 10x + -10x + x2 + -1x2 Combine like terms: 24 + -24 = 0 -24 + -2x + 1x2 = 0 + 10x + -10x + x2 + -1x2 -24 + -2x + 1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -24 + -2x + 1x2 = 0 + x2 + -1x2 -24 + -2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -24 + -2x + 1x2 = 0 Factor a trinomial. (-4 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
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 = 6Solution
x = {-4, 6}
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