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Simplifying (9x + 3)(5x + 6) = 0 Reorder the terms: (3 + 9x)(5x + 6) = 0 Reorder the terms: (3 + 9x)(6 + 5x) = 0 Multiply (3 + 9x) * (6 + 5x) (3(6 + 5x) + 9x * (6 + 5x)) = 0 ((6 * 3 + 5x * 3) + 9x * (6 + 5x)) = 0 ((18 + 15x) + 9x * (6 + 5x)) = 0 (18 + 15x + (6 * 9x + 5x * 9x)) = 0 (18 + 15x + (54x + 45x2)) = 0 Combine like terms: 15x + 54x = 69x (18 + 69x + 45x2) = 0 Solving 18 + 69x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 23x + 15x2) = 0 Factor a trinomial. 3((6 + 5x)(1 + 3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + 5x)' equal to zero and attempt to solve: Simplifying 6 + 5x = 0 Solving 6 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x = 0 + -6 5x = 0 + -6 Combine like terms: 0 + -6 = -6 5x = -6 Divide each side by '5'. x = -1.2 Simplifying x = -1.2Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-1.2, -0.3333333333}
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