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Simplifying 3(6 + -7x)(10x + 7) = 0 Reorder the terms: 3(6 + -7x)(7 + 10x) = 0 Multiply (6 + -7x) * (7 + 10x) 3(6(7 + 10x) + -7x * (7 + 10x)) = 0 3((7 * 6 + 10x * 6) + -7x * (7 + 10x)) = 0 3((42 + 60x) + -7x * (7 + 10x)) = 0 3(42 + 60x + (7 * -7x + 10x * -7x)) = 0 3(42 + 60x + (-49x + -70x2)) = 0 Combine like terms: 60x + -49x = 11x 3(42 + 11x + -70x2) = 0 (42 * 3 + 11x * 3 + -70x2 * 3) = 0 (126 + 33x + -210x2) = 0 Solving 126 + 33x + -210x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(42 + 11x + -70x2) = 0 Factor a trinomial. 3((6 + -7x)(7 + 10x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -7x)' equal to zero and attempt to solve: Simplifying 6 + -7x = 0 Solving 6 + -7x = 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 + -7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x = 0 + -6 -7x = 0 + -6 Combine like terms: 0 + -6 = -6 -7x = -6 Divide each side by '-7'. x = 0.8571428571 Simplifying x = 0.8571428571Subproblem 2
Set the factor '(7 + 10x)' equal to zero and attempt to solve: Simplifying 7 + 10x = 0 Solving 7 + 10x = 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 + 10x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 10x = 0 + -7 10x = 0 + -7 Combine like terms: 0 + -7 = -7 10x = -7 Divide each side by '10'. x = -0.7 Simplifying x = -0.7Solution
x = {0.8571428571, -0.7}
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