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Simplifying (7x + 35)(2x + -12) = 0 Reorder the terms: (35 + 7x)(2x + -12) = 0 Reorder the terms: (35 + 7x)(-12 + 2x) = 0 Multiply (35 + 7x) * (-12 + 2x) (35(-12 + 2x) + 7x * (-12 + 2x)) = 0 ((-12 * 35 + 2x * 35) + 7x * (-12 + 2x)) = 0 ((-420 + 70x) + 7x * (-12 + 2x)) = 0 (-420 + 70x + (-12 * 7x + 2x * 7x)) = 0 (-420 + 70x + (-84x + 14x2)) = 0 Combine like terms: 70x + -84x = -14x (-420 + -14x + 14x2) = 0 Solving -420 + -14x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '14'. 14(-30 + -1x + x2) = 0 Factor a trinomial. 14((-5 + -1x)(6 + -1x)) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-5, 6}
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