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Simplifying 3(7x + -5)(6x + 7) = 0 Reorder the terms: 3(-5 + 7x)(6x + 7) = 0 Reorder the terms: 3(-5 + 7x)(7 + 6x) = 0 Multiply (-5 + 7x) * (7 + 6x) 3(-5(7 + 6x) + 7x * (7 + 6x)) = 0 3((7 * -5 + 6x * -5) + 7x * (7 + 6x)) = 0 3((-35 + -30x) + 7x * (7 + 6x)) = 0 3(-35 + -30x + (7 * 7x + 6x * 7x)) = 0 3(-35 + -30x + (49x + 42x2)) = 0 Combine like terms: -30x + 49x = 19x 3(-35 + 19x + 42x2) = 0 (-35 * 3 + 19x * 3 + 42x2 * 3) = 0 (-105 + 57x + 126x2) = 0 Solving -105 + 57x + 126x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-35 + 19x + 42x2) = 0 Factor a trinomial. 3((-7 + -6x)(5 + -7x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -6x)' equal to zero and attempt to solve: Simplifying -7 + -6x = 0 Solving -7 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -6x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6x = 0 + 7 -6x = 0 + 7 Combine like terms: 0 + 7 = 7 -6x = 7 Divide each side by '-6'. x = -1.166666667 Simplifying x = -1.166666667Subproblem 2
Set the factor '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 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 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143Solution
x = {-1.166666667, 0.7142857143}
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