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Simplifying -8x(4 + 6x) + 8x(4x + 7) = 0 (4 * -8x + 6x * -8x) + 8x(4x + 7) = 0 (-32x + -48x2) + 8x(4x + 7) = 0 Reorder the terms: -32x + -48x2 + 8x(7 + 4x) = 0 -32x + -48x2 + (7 * 8x + 4x * 8x) = 0 -32x + -48x2 + (56x + 32x2) = 0 Reorder the terms: -32x + 56x + -48x2 + 32x2 = 0 Combine like terms: -32x + 56x = 24x 24x + -48x2 + 32x2 = 0 Combine like terms: -48x2 + 32x2 = -16x2 24x + -16x2 = 0 Solving 24x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x'. 8x(3 + -2x) = 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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5}
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