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Simplifying (6x + -3)(8x + 3) = 0 Reorder the terms: (-3 + 6x)(8x + 3) = 0 Reorder the terms: (-3 + 6x)(3 + 8x) = 0 Multiply (-3 + 6x) * (3 + 8x) (-3(3 + 8x) + 6x * (3 + 8x)) = 0 ((3 * -3 + 8x * -3) + 6x * (3 + 8x)) = 0 ((-9 + -24x) + 6x * (3 + 8x)) = 0 (-9 + -24x + (3 * 6x + 8x * 6x)) = 0 (-9 + -24x + (18x + 48x2)) = 0 Combine like terms: -24x + 18x = -6x (-9 + -6x + 48x2) = 0 Solving -9 + -6x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -2x + 16x2) = 0 Factor a trinomial. 3((-3 + -8x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -8x)' equal to zero and attempt to solve: Simplifying -3 + -8x = 0 Solving -3 + -8x = 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 + -8x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8x = 0 + 3 -8x = 0 + 3 Combine like terms: 0 + 3 = 3 -8x = 3 Divide each side by '-8'. x = -0.375 Simplifying x = -0.375Subproblem 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 = {-0.375, 0.5}
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