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Simplifying 3(4 + -7x)(8x + 3) = 0 Reorder the terms: 3(4 + -7x)(3 + 8x) = 0 Multiply (4 + -7x) * (3 + 8x) 3(4(3 + 8x) + -7x * (3 + 8x)) = 0 3((3 * 4 + 8x * 4) + -7x * (3 + 8x)) = 0 3((12 + 32x) + -7x * (3 + 8x)) = 0 3(12 + 32x + (3 * -7x + 8x * -7x)) = 0 3(12 + 32x + (-21x + -56x2)) = 0 Combine like terms: 32x + -21x = 11x 3(12 + 11x + -56x2) = 0 (12 * 3 + 11x * 3 + -56x2 * 3) = 0 (36 + 33x + -168x2) = 0 Solving 36 + 33x + -168x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 11x + -56x2) = 0 Factor a trinomial. 3((4 + -7x)(3 + 8x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -7x)' equal to zero and attempt to solve: Simplifying 4 + -7x = 0 Solving 4 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7x = 0 + -4 -7x = 0 + -4 Combine like terms: 0 + -4 = -4 -7x = -4 Divide each side by '-7'. x = 0.5714285714 Simplifying x = 0.5714285714Subproblem 2
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 = -0.375Solution
x = {0.5714285714, -0.375}
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