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Simplifying 42x2 + 186x + 180 = 0 Reorder the terms: 180 + 186x + 42x2 = 0 Solving 180 + 186x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(30 + 31x + 7x2) = 0 Factor a trinomial. 6((3 + x)(10 + 7x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(10 + 7x)' equal to zero and attempt to solve: Simplifying 10 + 7x = 0 Solving 10 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 7x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 7x = 0 + -10 7x = 0 + -10 Combine like terms: 0 + -10 = -10 7x = -10 Divide each side by '7'. x = -1.428571429 Simplifying x = -1.428571429Solution
x = {-3, -1.428571429}
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