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Simplifying (5x + 1)(2x + 3) = 0 Reorder the terms: (1 + 5x)(2x + 3) = 0 Reorder the terms: (1 + 5x)(3 + 2x) = 0 Multiply (1 + 5x) * (3 + 2x) (1(3 + 2x) + 5x * (3 + 2x)) = 0 ((3 * 1 + 2x * 1) + 5x * (3 + 2x)) = 0 ((3 + 2x) + 5x * (3 + 2x)) = 0 (3 + 2x + (3 * 5x + 2x * 5x)) = 0 (3 + 2x + (15x + 10x2)) = 0 Combine like terms: 2x + 15x = 17x (3 + 17x + 10x2) = 0 Solving 3 + 17x + 10x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + 2x)(1 + 5x) = 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 '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Solution
x = {-1.5, -0.2}
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