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Simplifying 5(6x2 + 15x + 9) = 0 Reorder the terms: 5(9 + 15x + 6x2) = 0 (9 * 5 + 15x * 5 + 6x2 * 5) = 0 (45 + 75x + 30x2) = 0 Solving 45 + 75x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(3 + 5x + 2x2) = 0 Factor a trinomial. 15((3 + 2x)(1 + x)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, -1}
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