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Simplifying x(x + 5) = x(2x + 4) Reorder the terms: x(5 + x) = x(2x + 4) (5 * x + x * x) = x(2x + 4) (5x + x2) = x(2x + 4) Reorder the terms: 5x + x2 = x(4 + 2x) 5x + x2 = (4 * x + 2x * x) 5x + x2 = (4x + 2x2) Solving 5x + x2 = 4x + 2x2 Solving for variable 'x'. Reorder the terms: 5x + -4x + x2 + -2x2 = 4x + 2x2 + -4x + -2x2 Combine like terms: 5x + -4x = 1x 1x + x2 + -2x2 = 4x + 2x2 + -4x + -2x2 Combine like terms: x2 + -2x2 = -1x2 1x + -1x2 = 4x + 2x2 + -4x + -2x2 Reorder the terms: 1x + -1x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 1x + -1x2 = 0 + 2x2 + -2x2 1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -1x) = 0Subproblem 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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