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Simplifying (8x + -4)(-8x + 6) = 0 Reorder the terms: (-4 + 8x)(-8x + 6) = 0 Reorder the terms: (-4 + 8x)(6 + -8x) = 0 Multiply (-4 + 8x) * (6 + -8x) (-4(6 + -8x) + 8x * (6 + -8x)) = 0 ((6 * -4 + -8x * -4) + 8x * (6 + -8x)) = 0 ((-24 + 32x) + 8x * (6 + -8x)) = 0 (-24 + 32x + (6 * 8x + -8x * 8x)) = 0 (-24 + 32x + (48x + -64x2)) = 0 Combine like terms: 32x + 48x = 80x (-24 + 80x + -64x2) = 0 Solving -24 + 80x + -64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-3 + 10x + -8x2) = 0 Factor a trinomial. 8((-3 + 4x)(1 + -2x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + 4x)' equal to zero and attempt to solve: Simplifying -3 + 4x = 0 Solving -3 + 4x = 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 + 4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x = 0 + 3 4x = 0 + 3 Combine like terms: 0 + 3 = 3 4x = 3 Divide each side by '4'. x = 0.75 Simplifying x = 0.75Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {0.75, 0.5}
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