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Simplifying (7x + -27)(4x + 12) = 0 Reorder the terms: (-27 + 7x)(4x + 12) = 0 Reorder the terms: (-27 + 7x)(12 + 4x) = 0 Multiply (-27 + 7x) * (12 + 4x) (-27(12 + 4x) + 7x * (12 + 4x)) = 0 ((12 * -27 + 4x * -27) + 7x * (12 + 4x)) = 0 ((-324 + -108x) + 7x * (12 + 4x)) = 0 (-324 + -108x + (12 * 7x + 4x * 7x)) = 0 (-324 + -108x + (84x + 28x2)) = 0 Combine like terms: -108x + 84x = -24x (-324 + -24x + 28x2) = 0 Solving -324 + -24x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-81 + -6x + 7x2) = 0 Factor a trinomial. 4((-3 + -1x)(27 + -7x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(27 + -7x)' equal to zero and attempt to solve: Simplifying 27 + -7x = 0 Solving 27 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -7x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -7x = 0 + -27 -7x = 0 + -27 Combine like terms: 0 + -27 = -27 -7x = -27 Divide each side by '-7'. x = 3.857142857 Simplifying x = 3.857142857Solution
x = {-3, 3.857142857}
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