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Simplifying 2x(1x + 5) = 4x(2x + 10) Reorder the terms: 2x(5 + 1x) = 4x(2x + 10) (5 * 2x + 1x * 2x) = 4x(2x + 10) (10x + 2x2) = 4x(2x + 10) Reorder the terms: 10x + 2x2 = 4x(10 + 2x) 10x + 2x2 = (10 * 4x + 2x * 4x) 10x + 2x2 = (40x + 8x2) Solving 10x + 2x2 = 40x + 8x2 Solving for variable 'x'. Reorder the terms: 10x + -40x + 2x2 + -8x2 = 40x + 8x2 + -40x + -8x2 Combine like terms: 10x + -40x = -30x -30x + 2x2 + -8x2 = 40x + 8x2 + -40x + -8x2 Combine like terms: 2x2 + -8x2 = -6x2 -30x + -6x2 = 40x + 8x2 + -40x + -8x2 Reorder the terms: -30x + -6x2 = 40x + -40x + 8x2 + -8x2 Combine like terms: 40x + -40x = 0 -30x + -6x2 = 0 + 8x2 + -8x2 -30x + -6x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -30x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-6x'. -6x(5 + x) = 0 Ignore the factor -6.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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {0, -5}
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