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Simplifying (3x + 6)(5x + 4) = 0 Reorder the terms: (6 + 3x)(5x + 4) = 0 Reorder the terms: (6 + 3x)(4 + 5x) = 0 Multiply (6 + 3x) * (4 + 5x) (6(4 + 5x) + 3x * (4 + 5x)) = 0 ((4 * 6 + 5x * 6) + 3x * (4 + 5x)) = 0 ((24 + 30x) + 3x * (4 + 5x)) = 0 (24 + 30x + (4 * 3x + 5x * 3x)) = 0 (24 + 30x + (12x + 15x2)) = 0 Combine like terms: 30x + 12x = 42x (24 + 42x + 15x2) = 0 Solving 24 + 42x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 14x + 5x2) = 0 Factor a trinomial. 3((2 + x)(4 + 5x)) = 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 '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Divide each side by '5'. x = -0.8 Simplifying x = -0.8Solution
x = {-2, -0.8}
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