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Simplifying (x + 5) * x(x + 3) = 0 Reorder the terms: (5 + x) * x(x + 3) = 0 Reorder the terms: (5 + x) * x(3 + x) = 0 Reorder the terms for easier multiplication: x(5 + x)(3 + x) = 0 Multiply (5 + x) * (3 + x) x(5(3 + x) + x(3 + x)) = 0 x((3 * 5 + x * 5) + x(3 + x)) = 0 x((15 + 5x) + x(3 + x)) = 0 x(15 + 5x + (3 * x + x * x)) = 0 x(15 + 5x + (3x + x2)) = 0 Combine like terms: 5x + 3x = 8x x(15 + 8x + x2) = 0 (15 * x + 8x * x + x2 * x) = 0 (15x + 8x2 + x3) = 0 Solving 15x + 8x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(15 + 8x + x2) = 0 Factor a trinomial. x((5 + x)(3 + x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 3
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 = -3Solution
x = {0, -5, -3}
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