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Simplifying (3x + 6)(5x + 10) = 0 Reorder the terms: (6 + 3x)(5x + 10) = 0 Reorder the terms: (6 + 3x)(10 + 5x) = 0 Multiply (6 + 3x) * (10 + 5x) (6(10 + 5x) + 3x * (10 + 5x)) = 0 ((10 * 6 + 5x * 6) + 3x * (10 + 5x)) = 0 ((60 + 30x) + 3x * (10 + 5x)) = 0 (60 + 30x + (10 * 3x + 5x * 3x)) = 0 (60 + 30x + (30x + 15x2)) = 0 Combine like terms: 30x + 30x = 60x (60 + 60x + 15x2) = 0 Solving 60 + 60x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(4 + 4x + x2) = 0 Factor a trinomial. 15((2 + x)(2 + x)) = 0 Ignore the factor 15.Subproblem 1
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 = -2Subproblem 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 = {-2, -2}
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