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Simplifying (7x + -5)(6x + 9) = 0 Reorder the terms: (-5 + 7x)(6x + 9) = 0 Reorder the terms: (-5 + 7x)(9 + 6x) = 0 Multiply (-5 + 7x) * (9 + 6x) (-5(9 + 6x) + 7x * (9 + 6x)) = 0 ((9 * -5 + 6x * -5) + 7x * (9 + 6x)) = 0 ((-45 + -30x) + 7x * (9 + 6x)) = 0 (-45 + -30x + (9 * 7x + 6x * 7x)) = 0 (-45 + -30x + (63x + 42x2)) = 0 Combine like terms: -30x + 63x = 33x (-45 + 33x + 42x2) = 0 Solving -45 + 33x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 11x + 14x2) = 0 Factor a trinomial. 3((-3 + -2x)(5 + -7x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, 0.7142857143}
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