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Simplifying 4x(x + -1) + -7x(x + -6) = 5x(x + 6) Reorder the terms: 4x(-1 + x) + -7x(x + -6) = 5x(x + 6) (-1 * 4x + x * 4x) + -7x(x + -6) = 5x(x + 6) (-4x + 4x2) + -7x(x + -6) = 5x(x + 6) Reorder the terms: -4x + 4x2 + -7x(-6 + x) = 5x(x + 6) -4x + 4x2 + (-6 * -7x + x * -7x) = 5x(x + 6) -4x + 4x2 + (42x + -7x2) = 5x(x + 6) Reorder the terms: -4x + 42x + 4x2 + -7x2 = 5x(x + 6) Combine like terms: -4x + 42x = 38x 38x + 4x2 + -7x2 = 5x(x + 6) Combine like terms: 4x2 + -7x2 = -3x2 38x + -3x2 = 5x(x + 6) Reorder the terms: 38x + -3x2 = 5x(6 + x) 38x + -3x2 = (6 * 5x + x * 5x) 38x + -3x2 = (30x + 5x2) Solving 38x + -3x2 = 30x + 5x2 Solving for variable 'x'. Reorder the terms: 38x + -30x + -3x2 + -5x2 = 30x + 5x2 + -30x + -5x2 Combine like terms: 38x + -30x = 8x 8x + -3x2 + -5x2 = 30x + 5x2 + -30x + -5x2 Combine like terms: -3x2 + -5x2 = -8x2 8x + -8x2 = 30x + 5x2 + -30x + -5x2 Reorder the terms: 8x + -8x2 = 30x + -30x + 5x2 + -5x2 Combine like terms: 30x + -30x = 0 8x + -8x2 = 0 + 5x2 + -5x2 8x + -8x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 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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