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Simplifying (x + 4)(x + 8) = (2x + 4)(2x + 8) Reorder the terms: (4 + x)(x + 8) = (2x + 4)(2x + 8) Reorder the terms: (4 + x)(8 + x) = (2x + 4)(2x + 8) Multiply (4 + x) * (8 + x) (4(8 + x) + x(8 + x)) = (2x + 4)(2x + 8) ((8 * 4 + x * 4) + x(8 + x)) = (2x + 4)(2x + 8) ((32 + 4x) + x(8 + x)) = (2x + 4)(2x + 8) (32 + 4x + (8 * x + x * x)) = (2x + 4)(2x + 8) (32 + 4x + (8x + x2)) = (2x + 4)(2x + 8) Combine like terms: 4x + 8x = 12x (32 + 12x + x2) = (2x + 4)(2x + 8) Reorder the terms: 32 + 12x + x2 = (4 + 2x)(2x + 8) Reorder the terms: 32 + 12x + x2 = (4 + 2x)(8 + 2x) Multiply (4 + 2x) * (8 + 2x) 32 + 12x + x2 = (4(8 + 2x) + 2x * (8 + 2x)) 32 + 12x + x2 = ((8 * 4 + 2x * 4) + 2x * (8 + 2x)) 32 + 12x + x2 = ((32 + 8x) + 2x * (8 + 2x)) 32 + 12x + x2 = (32 + 8x + (8 * 2x + 2x * 2x)) 32 + 12x + x2 = (32 + 8x + (16x + 4x2)) Combine like terms: 8x + 16x = 24x 32 + 12x + x2 = (32 + 24x + 4x2) Add '-32' to each side of the equation. 32 + 12x + -32 + x2 = 32 + 24x + -32 + 4x2 Reorder the terms: 32 + -32 + 12x + x2 = 32 + 24x + -32 + 4x2 Combine like terms: 32 + -32 = 0 0 + 12x + x2 = 32 + 24x + -32 + 4x2 12x + x2 = 32 + 24x + -32 + 4x2 Reorder the terms: 12x + x2 = 32 + -32 + 24x + 4x2 Combine like terms: 32 + -32 = 0 12x + x2 = 0 + 24x + 4x2 12x + x2 = 24x + 4x2 Solving 12x + x2 = 24x + 4x2 Solving for variable 'x'. Reorder the terms: 12x + -24x + x2 + -4x2 = 24x + 4x2 + -24x + -4x2 Combine like terms: 12x + -24x = -12x -12x + x2 + -4x2 = 24x + 4x2 + -24x + -4x2 Combine like terms: x2 + -4x2 = -3x2 -12x + -3x2 = 24x + 4x2 + -24x + -4x2 Reorder the terms: -12x + -3x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 -12x + -3x2 = 0 + 4x2 + -4x2 -12x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -12x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3x'. -3x(4 + x) = 0 Ignore the factor -3.Subproblem 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0, -4}
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