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Simplifying (5x + 5)(3x + 1) = 0 Reorder the terms: (5 + 5x)(3x + 1) = 0 Reorder the terms: (5 + 5x)(1 + 3x) = 0 Multiply (5 + 5x) * (1 + 3x) (5(1 + 3x) + 5x * (1 + 3x)) = 0 ((1 * 5 + 3x * 5) + 5x * (1 + 3x)) = 0 ((5 + 15x) + 5x * (1 + 3x)) = 0 (5 + 15x + (1 * 5x + 3x * 5x)) = 0 (5 + 15x + (5x + 15x2)) = 0 Combine like terms: 15x + 5x = 20x (5 + 20x + 15x2) = 0 Solving 5 + 20x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 4x + 3x2) = 0 Factor a trinomial. 5((1 + x)(1 + 3x)) = 0 Ignore the factor 5.Subproblem 1
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 = -1Subproblem 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, -0.3333333333}
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