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Simplifying (4x + 30)(6x + 6) = 0 Reorder the terms: (30 + 4x)(6x + 6) = 0 Reorder the terms: (30 + 4x)(6 + 6x) = 0 Multiply (30 + 4x) * (6 + 6x) (30(6 + 6x) + 4x * (6 + 6x)) = 0 ((6 * 30 + 6x * 30) + 4x * (6 + 6x)) = 0 ((180 + 180x) + 4x * (6 + 6x)) = 0 (180 + 180x + (6 * 4x + 6x * 4x)) = 0 (180 + 180x + (24x + 24x2)) = 0 Combine like terms: 180x + 24x = 204x (180 + 204x + 24x2) = 0 Solving 180 + 204x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(15 + 17x + 2x2) = 0 Factor a trinomial. 12((15 + 2x)(1 + x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(15 + 2x)' equal to zero and attempt to solve: Simplifying 15 + 2x = 0 Solving 15 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2x = 0 + -15 2x = 0 + -15 Combine like terms: 0 + -15 = -15 2x = -15 Divide each side by '2'. x = -7.5 Simplifying x = -7.5Subproblem 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 = {-7.5, -1}
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