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Simplifying (3x + 4)(2x + 3) = 0 Reorder the terms: (4 + 3x)(2x + 3) = 0 Reorder the terms: (4 + 3x)(3 + 2x) = 0 Multiply (4 + 3x) * (3 + 2x) (4(3 + 2x) + 3x * (3 + 2x)) = 0 ((3 * 4 + 2x * 4) + 3x * (3 + 2x)) = 0 ((12 + 8x) + 3x * (3 + 2x)) = 0 (12 + 8x + (3 * 3x + 2x * 3x)) = 0 (12 + 8x + (9x + 6x2)) = 0 Combine like terms: 8x + 9x = 17x (12 + 17x + 6x2) = 0 Solving 12 + 17x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + 2x)(4 + 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 '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {-1.5, -1.333333333}
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