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Simplifying 7(x + 6)(3x + 1) = 0 Reorder the terms: 7(6 + x)(3x + 1) = 0 Reorder the terms: 7(6 + x)(1 + 3x) = 0 Multiply (6 + x) * (1 + 3x) 7(6(1 + 3x) + x(1 + 3x)) = 0 7((1 * 6 + 3x * 6) + x(1 + 3x)) = 0 7((6 + 18x) + x(1 + 3x)) = 0 7(6 + 18x + (1 * x + 3x * x)) = 0 7(6 + 18x + (1x + 3x2)) = 0 Combine like terms: 18x + 1x = 19x 7(6 + 19x + 3x2) = 0 (6 * 7 + 19x * 7 + 3x2 * 7) = 0 (42 + 133x + 21x2) = 0 Solving 42 + 133x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(6 + 19x + 3x2) = 0 Factor a trinomial. 7((6 + x)(1 + 3x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-6, -0.3333333333}
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