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Simplifying (2x + 3)(4x + 5) = 0 Reorder the terms: (3 + 2x)(4x + 5) = 0 Reorder the terms: (3 + 2x)(5 + 4x) = 0 Multiply (3 + 2x) * (5 + 4x) (3(5 + 4x) + 2x * (5 + 4x)) = 0 ((5 * 3 + 4x * 3) + 2x * (5 + 4x)) = 0 ((15 + 12x) + 2x * (5 + 4x)) = 0 (15 + 12x + (5 * 2x + 4x * 2x)) = 0 (15 + 12x + (10x + 8x2)) = 0 Combine like terms: 12x + 10x = 22x (15 + 22x + 8x2) = 0 Solving 15 + 22x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + 2x)(5 + 4x) = 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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25Solution
x = {-1.5, -1.25}
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