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Simplifying 3x(x + 5) + 6(x + 5) = 0 Reorder the terms: 3x(5 + x) + 6(x + 5) = 0 (5 * 3x + x * 3x) + 6(x + 5) = 0 (15x + 3x2) + 6(x + 5) = 0 Reorder the terms: 15x + 3x2 + 6(5 + x) = 0 15x + 3x2 + (5 * 6 + x * 6) = 0 15x + 3x2 + (30 + 6x) = 0 Reorder the terms: 30 + 15x + 6x + 3x2 = 0 Combine like terms: 15x + 6x = 21x 30 + 21x + 3x2 = 0 Solving 30 + 21x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 7x + x2) = 0 Factor a trinomial. 3((5 + x)(2 + x)) = 0 Ignore the factor 3.Subproblem 1
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 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-5, -2}
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