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Simplifying (2X + 3)(5X + 10) = 0 Reorder the terms: (3 + 2X)(5X + 10) = 0 Reorder the terms: (3 + 2X)(10 + 5X) = 0 Multiply (3 + 2X) * (10 + 5X) (3(10 + 5X) + 2X * (10 + 5X)) = 0 ((10 * 3 + 5X * 3) + 2X * (10 + 5X)) = 0 ((30 + 15X) + 2X * (10 + 5X)) = 0 (30 + 15X + (10 * 2X + 5X * 2X)) = 0 (30 + 15X + (20X + 10X2)) = 0 Combine like terms: 15X + 20X = 35X (30 + 35X + 10X2) = 0 Solving 30 + 35X + 10X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '5'. 5(6 + 7X + 2X2) = 0 Factor a trinomial. 5((2 + X)(3 + 2X)) = 0 Ignore the factor 5.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 '(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 = -1.5Solution
X = {-2, -1.5}
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