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Simplifying (2x + 5)(4x + 6) = 0 Reorder the terms: (5 + 2x)(4x + 6) = 0 Reorder the terms: (5 + 2x)(6 + 4x) = 0 Multiply (5 + 2x) * (6 + 4x) (5(6 + 4x) + 2x * (6 + 4x)) = 0 ((6 * 5 + 4x * 5) + 2x * (6 + 4x)) = 0 ((30 + 20x) + 2x * (6 + 4x)) = 0 (30 + 20x + (6 * 2x + 4x * 2x)) = 0 (30 + 20x + (12x + 8x2)) = 0 Combine like terms: 20x + 12x = 32x (30 + 32x + 8x2) = 0 Solving 30 + 32x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 16x + 4x2) = 0 Factor a trinomial. 2((5 + 2x)(3 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 2
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 = -1.5Solution
x = {-2.5, -1.5}
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