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Simplifying (4x + 5)(3x + 6) = 0 Reorder the terms: (5 + 4x)(3x + 6) = 0 Reorder the terms: (5 + 4x)(6 + 3x) = 0 Multiply (5 + 4x) * (6 + 3x) (5(6 + 3x) + 4x * (6 + 3x)) = 0 ((6 * 5 + 3x * 5) + 4x * (6 + 3x)) = 0 ((30 + 15x) + 4x * (6 + 3x)) = 0 (30 + 15x + (6 * 4x + 3x * 4x)) = 0 (30 + 15x + (24x + 12x2)) = 0 Combine like terms: 15x + 24x = 39x (30 + 39x + 12x2) = 0 Solving 30 + 39x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 13x + 4x2) = 0 Factor a trinomial. 3((2 + x)(5 + 4x)) = 0 Ignore the factor 3.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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25Solution
x = {-2, -1.25}
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