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Simplifying 3(X + 1)(2X + 5) = 0 Reorder the terms: 3(1 + X)(2X + 5) = 0 Reorder the terms: 3(1 + X)(5 + 2X) = 0 Multiply (1 + X) * (5 + 2X) 3(1(5 + 2X) + X(5 + 2X)) = 0 3((5 * 1 + 2X * 1) + X(5 + 2X)) = 0 3((5 + 2X) + X(5 + 2X)) = 0 3(5 + 2X + (5 * X + 2X * X)) = 0 3(5 + 2X + (5X + 2X2)) = 0 Combine like terms: 2X + 5X = 7X 3(5 + 7X + 2X2) = 0 (5 * 3 + 7X * 3 + 2X2 * 3) = 0 (15 + 21X + 6X2) = 0 Solving 15 + 21X + 6X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 7X + 2X2) = 0 Factor a trinomial. 3((5 + 2X)(1 + X)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 2X)' equal to zero and attempt to solve: Simplifying 5 + 2X = 0 Solving 5 + 2X = 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 + 2X = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2X = 0 + -5 2X = 0 + -5 Combine like terms: 0 + -5 = -5 2X = -5 Divide each side by '2'. X = -2.5 Simplifying X = -2.5Subproblem 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 = {-2.5, -1}
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