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Simplifying (3x + 6)(2x + 10) = 0 Reorder the terms: (6 + 3x)(2x + 10) = 0 Reorder the terms: (6 + 3x)(10 + 2x) = 0 Multiply (6 + 3x) * (10 + 2x) (6(10 + 2x) + 3x * (10 + 2x)) = 0 ((10 * 6 + 2x * 6) + 3x * (10 + 2x)) = 0 ((60 + 12x) + 3x * (10 + 2x)) = 0 (60 + 12x + (10 * 3x + 2x * 3x)) = 0 (60 + 12x + (30x + 6x2)) = 0 Combine like terms: 12x + 30x = 42x (60 + 42x + 6x2) = 0 Solving 60 + 42x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(10 + 7x + x2) = 0 Factor a trinomial. 6((5 + x)(2 + x)) = 0 Ignore the factor 6.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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