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Simplifying 3(2x + -1)(14x + -9) = 0 Reorder the terms: 3(-1 + 2x)(14x + -9) = 0 Reorder the terms: 3(-1 + 2x)(-9 + 14x) = 0 Multiply (-1 + 2x) * (-9 + 14x) 3(-1(-9 + 14x) + 2x * (-9 + 14x)) = 0 3((-9 * -1 + 14x * -1) + 2x * (-9 + 14x)) = 0 3((9 + -14x) + 2x * (-9 + 14x)) = 0 3(9 + -14x + (-9 * 2x + 14x * 2x)) = 0 3(9 + -14x + (-18x + 28x2)) = 0 Combine like terms: -14x + -18x = -32x 3(9 + -32x + 28x2) = 0 (9 * 3 + -32x * 3 + 28x2 * 3) = 0 (27 + -96x + 84x2) = 0 Solving 27 + -96x + 84x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -32x + 28x2) = 0 Factor a trinomial. 3((1 + -2x)(9 + -14x)) = 0 Ignore the factor 3.Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(9 + -14x)' equal to zero and attempt to solve: Simplifying 9 + -14x = 0 Solving 9 + -14x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -14x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -14x = 0 + -9 -14x = 0 + -9 Combine like terms: 0 + -9 = -9 -14x = -9 Divide each side by '-14'. x = 0.6428571429 Simplifying x = 0.6428571429Solution
x = {0.5, 0.6428571429}
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