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Simplifying 5(2x + 3)(x + 1) = 0 Reorder the terms: 5(3 + 2x)(x + 1) = 0 Reorder the terms: 5(3 + 2x)(1 + x) = 0 Multiply (3 + 2x) * (1 + x) 5(3(1 + x) + 2x * (1 + x)) = 0 5((1 * 3 + x * 3) + 2x * (1 + x)) = 0 5((3 + 3x) + 2x * (1 + x)) = 0 5(3 + 3x + (1 * 2x + x * 2x)) = 0 5(3 + 3x + (2x + 2x2)) = 0 Combine like terms: 3x + 2x = 5x 5(3 + 5x + 2x2) = 0 (3 * 5 + 5x * 5 + 2x2 * 5) = 0 (15 + 25x + 10x2) = 0 Solving 15 + 25x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + 5x + 2x2) = 0 Factor a trinomial. 5((3 + 2x)(1 + x)) = 0 Ignore the factor 5.Subproblem 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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-1.5, -1}
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