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Simplifying (6x + -4)(8x + 3) = 0 Reorder the terms: (-4 + 6x)(8x + 3) = 0 Reorder the terms: (-4 + 6x)(3 + 8x) = 0 Multiply (-4 + 6x) * (3 + 8x) (-4(3 + 8x) + 6x * (3 + 8x)) = 0 ((3 * -4 + 8x * -4) + 6x * (3 + 8x)) = 0 ((-12 + -32x) + 6x * (3 + 8x)) = 0 (-12 + -32x + (3 * 6x + 8x * 6x)) = 0 (-12 + -32x + (18x + 48x2)) = 0 Combine like terms: -32x + 18x = -14x (-12 + -14x + 48x2) = 0 Solving -12 + -14x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -7x + 24x2) = 0 Factor a trinomial. 2((-3 + -8x)(2 + -3x)) = 0 Ignore the factor 2.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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-0.375, 0.6666666667}
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