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Simplifying (3x + 2)(2x + 3) = 0 Reorder the terms: (2 + 3x)(2x + 3) = 0 Reorder the terms: (2 + 3x)(3 + 2x) = 0 Multiply (2 + 3x) * (3 + 2x) (2(3 + 2x) + 3x * (3 + 2x)) = 0 ((3 * 2 + 2x * 2) + 3x * (3 + 2x)) = 0 ((6 + 4x) + 3x * (3 + 2x)) = 0 (6 + 4x + (3 * 3x + 2x * 3x)) = 0 (6 + 4x + (9x + 6x2)) = 0 Combine like terms: 4x + 9x = 13x (6 + 13x + 6x2) = 0 Solving 6 + 13x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + 2x)(2 + 3x) = 0Subproblem 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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-1.5, -0.6666666667}
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