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Simplifying x(3x + 4) = 4x(x + -1) Reorder the terms: x(4 + 3x) = 4x(x + -1) (4 * x + 3x * x) = 4x(x + -1) (4x + 3x2) = 4x(x + -1) Reorder the terms: 4x + 3x2 = 4x(-1 + x) 4x + 3x2 = (-1 * 4x + x * 4x) 4x + 3x2 = (-4x + 4x2) Solving 4x + 3x2 = -4x + 4x2 Solving for variable 'x'. Reorder the terms: 4x + 4x + 3x2 + -4x2 = -4x + 4x2 + 4x + -4x2 Combine like terms: 4x + 4x = 8x 8x + 3x2 + -4x2 = -4x + 4x2 + 4x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 8x + -1x2 = -4x + 4x2 + 4x + -4x2 Reorder the terms: 8x + -1x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 8x + -1x2 = 0 + 4x2 + -4x2 8x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(8 + -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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {0, 8}
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