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Simplifying (8x + -6)(2x + 3) = 0 Reorder the terms: (-6 + 8x)(2x + 3) = 0 Reorder the terms: (-6 + 8x)(3 + 2x) = 0 Multiply (-6 + 8x) * (3 + 2x) (-6(3 + 2x) + 8x * (3 + 2x)) = 0 ((3 * -6 + 2x * -6) + 8x * (3 + 2x)) = 0 ((-18 + -12x) + 8x * (3 + 2x)) = 0 (-18 + -12x + (3 * 8x + 2x * 8x)) = 0 (-18 + -12x + (24x + 16x2)) = 0 Combine like terms: -12x + 24x = 12x (-18 + 12x + 16x2) = 0 Solving -18 + 12x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 6x + 8x2) = 0 Factor a trinomial. 2((-3 + -2x)(3 + -4x)) = 0 Ignore the factor 2.Subproblem 1
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 = -1.5Subproblem 2
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 = 0.75Solution
x = {-1.5, 0.75}
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