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Simplifying (3x + 1)(6 + -4x) = 0 Reorder the terms: (1 + 3x)(6 + -4x) = 0 Multiply (1 + 3x) * (6 + -4x) (1(6 + -4x) + 3x * (6 + -4x)) = 0 ((6 * 1 + -4x * 1) + 3x * (6 + -4x)) = 0 ((6 + -4x) + 3x * (6 + -4x)) = 0 (6 + -4x + (6 * 3x + -4x * 3x)) = 0 (6 + -4x + (18x + -12x2)) = 0 Combine like terms: -4x + 18x = 14x (6 + 14x + -12x2) = 0 Solving 6 + 14x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 7x + -6x2) = 0 Factor a trinomial. 2((3 + -2x)(1 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 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 = {1.5, -0.3333333333}
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