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Simplifying (3x + 5)(4x + 2) = 0 Reorder the terms: (5 + 3x)(4x + 2) = 0 Reorder the terms: (5 + 3x)(2 + 4x) = 0 Multiply (5 + 3x) * (2 + 4x) (5(2 + 4x) + 3x * (2 + 4x)) = 0 ((2 * 5 + 4x * 5) + 3x * (2 + 4x)) = 0 ((10 + 20x) + 3x * (2 + 4x)) = 0 (10 + 20x + (2 * 3x + 4x * 3x)) = 0 (10 + 20x + (6x + 12x2)) = 0 Combine like terms: 20x + 6x = 26x (10 + 26x + 12x2) = 0 Solving 10 + 26x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 13x + 6x2) = 0 Factor a trinomial. 2((5 + 3x)(1 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1.666666667, -0.5}
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