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Simplifying (x)(32 + x) = (3x)(8 + 3x) (32 * x + x * x) = (3x)(8 + 3x) (32x + x2) = (3x)(8 + 3x) Remove parenthesis around (3x) 32x + x2 = 3x(8 + 3x) 32x + x2 = (8 * 3x + 3x * 3x) 32x + x2 = (24x + 9x2) Solving 32x + x2 = 24x + 9x2 Solving for variable 'x'. Reorder the terms: 32x + -24x + x2 + -9x2 = 24x + 9x2 + -24x + -9x2 Combine like terms: 32x + -24x = 8x 8x + x2 + -9x2 = 24x + 9x2 + -24x + -9x2 Combine like terms: x2 + -9x2 = -8x2 8x + -8x2 = 24x + 9x2 + -24x + -9x2 Reorder the terms: 8x + -8x2 = 24x + -24x + 9x2 + -9x2 Combine like terms: 24x + -24x = 0 8x + -8x2 = 0 + 9x2 + -9x2 8x + -8x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 8x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '8x'. 8x(1 + -1x) = 0 Ignore the factor 8.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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, 1}
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