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Simplifying 5(x + 1)(x + 3) = 0 Reorder the terms: 5(1 + x)(x + 3) = 0 Reorder the terms: 5(1 + x)(3 + x) = 0 Multiply (1 + x) * (3 + x) 5(1(3 + x) + x(3 + x)) = 0 5((3 * 1 + x * 1) + x(3 + x)) = 0 5((3 + 1x) + x(3 + x)) = 0 5(3 + 1x + (3 * x + x * x)) = 0 5(3 + 1x + (3x + x2)) = 0 Combine like terms: 1x + 3x = 4x 5(3 + 4x + x2) = 0 (3 * 5 + 4x * 5 + x2 * 5) = 0 (15 + 20x + 5x2) = 0 Solving 15 + 20x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + 4x + x2) = 0 Factor a trinomial. 5((3 + x)(1 + x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 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 = {-3, -1}
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