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Simplifying (3x + 1) * 12x = 360 Reorder the terms: (1 + 3x) * 12x = 360 Reorder the terms for easier multiplication: 12x(1 + 3x) = 360 (1 * 12x + 3x * 12x) = 360 (12x + 36x2) = 360 Solving 12x + 36x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 12x + 36x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 12x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-30 + x + 3x2) = 0 Factor a trinomial. 12((-10 + -3x)(3 + -1x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve: Simplifying -10 + -3x = 0 Solving -10 + -3x = 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 + -3x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3x = 0 + 10 -3x = 0 + 10 Combine like terms: 0 + 10 = 10 -3x = 10 Divide each side by '-3'. x = -3.333333333 Simplifying x = -3.333333333Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-3.333333333, 3}
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