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Simplifying (12x + 3)(9 + -1x) = 0 Reorder the terms: (3 + 12x)(9 + -1x) = 0 Multiply (3 + 12x) * (9 + -1x) (3(9 + -1x) + 12x * (9 + -1x)) = 0 ((9 * 3 + -1x * 3) + 12x * (9 + -1x)) = 0 ((27 + -3x) + 12x * (9 + -1x)) = 0 (27 + -3x + (9 * 12x + -1x * 12x)) = 0 (27 + -3x + (108x + -12x2)) = 0 Combine like terms: -3x + 108x = 105x (27 + 105x + -12x2) = 0 Solving 27 + 105x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 35x + -4x2) = 0 Factor a trinomial. 3((9 + -1x)(1 + 4x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {9, -0.25}
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