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Simplifying 6x(2x + 4) = (2x + 2)(2x + 12) Reorder the terms: 6x(4 + 2x) = (2x + 2)(2x + 12) (4 * 6x + 2x * 6x) = (2x + 2)(2x + 12) (24x + 12x2) = (2x + 2)(2x + 12) Reorder the terms: 24x + 12x2 = (2 + 2x)(2x + 12) Reorder the terms: 24x + 12x2 = (2 + 2x)(12 + 2x) Multiply (2 + 2x) * (12 + 2x) 24x + 12x2 = (2(12 + 2x) + 2x * (12 + 2x)) 24x + 12x2 = ((12 * 2 + 2x * 2) + 2x * (12 + 2x)) 24x + 12x2 = ((24 + 4x) + 2x * (12 + 2x)) 24x + 12x2 = (24 + 4x + (12 * 2x + 2x * 2x)) 24x + 12x2 = (24 + 4x + (24x + 4x2)) Combine like terms: 4x + 24x = 28x 24x + 12x2 = (24 + 28x + 4x2) Solving 24x + 12x2 = 24 + 28x + 4x2 Solving for variable 'x'. Reorder the terms: -24 + 24x + -28x + 12x2 + -4x2 = 24 + 28x + 4x2 + -24 + -28x + -4x2 Combine like terms: 24x + -28x = -4x -24 + -4x + 12x2 + -4x2 = 24 + 28x + 4x2 + -24 + -28x + -4x2 Combine like terms: 12x2 + -4x2 = 8x2 -24 + -4x + 8x2 = 24 + 28x + 4x2 + -24 + -28x + -4x2 Reorder the terms: -24 + -4x + 8x2 = 24 + -24 + 28x + -28x + 4x2 + -4x2 Combine like terms: 24 + -24 = 0 -24 + -4x + 8x2 = 0 + 28x + -28x + 4x2 + -4x2 -24 + -4x + 8x2 = 28x + -28x + 4x2 + -4x2 Combine like terms: 28x + -28x = 0 -24 + -4x + 8x2 = 0 + 4x2 + -4x2 -24 + -4x + 8x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -24 + -4x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -1x + 2x2) = 0 Factor a trinomial. 4((-3 + -2x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, 2}
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