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Simplifying (6x + 9)(4x + 3) = 0 Reorder the terms: (9 + 6x)(4x + 3) = 0 Reorder the terms: (9 + 6x)(3 + 4x) = 0 Multiply (9 + 6x) * (3 + 4x) (9(3 + 4x) + 6x * (3 + 4x)) = 0 ((3 * 9 + 4x * 9) + 6x * (3 + 4x)) = 0 ((27 + 36x) + 6x * (3 + 4x)) = 0 (27 + 36x + (3 * 6x + 4x * 6x)) = 0 (27 + 36x + (18x + 24x2)) = 0 Combine like terms: 36x + 18x = 54x (27 + 54x + 24x2) = 0 Solving 27 + 54x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 18x + 8x2) = 0 Factor a trinomial. 3((3 + 2x)(3 + 4x)) = 0 Ignore the factor 3.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 '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Solution
x = {-1.5, -0.75}
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