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Simplifying 6(2x + 3)(x + 1) = 0 Reorder the terms: 6(3 + 2x)(x + 1) = 0 Reorder the terms: 6(3 + 2x)(1 + x) = 0 Multiply (3 + 2x) * (1 + x) 6(3(1 + x) + 2x * (1 + x)) = 0 6((1 * 3 + x * 3) + 2x * (1 + x)) = 0 6((3 + 3x) + 2x * (1 + x)) = 0 6(3 + 3x + (1 * 2x + x * 2x)) = 0 6(3 + 3x + (2x + 2x2)) = 0 Combine like terms: 3x + 2x = 5x 6(3 + 5x + 2x2) = 0 (3 * 6 + 5x * 6 + 2x2 * 6) = 0 (18 + 30x + 12x2) = 0 Solving 18 + 30x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(3 + 5x + 2x2) = 0 Factor a trinomial. 6((3 + 2x)(1 + x)) = 0 Ignore the factor 6.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 '(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 = {-1.5, -1}
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