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Simplifying (3 + -2X)(4 + 2X) = 0 Multiply (3 + -2X) * (4 + 2X) (3(4 + 2X) + -2X * (4 + 2X)) = 0 ((4 * 3 + 2X * 3) + -2X * (4 + 2X)) = 0 ((12 + 6X) + -2X * (4 + 2X)) = 0 (12 + 6X + (4 * -2X + 2X * -2X)) = 0 (12 + 6X + (-8X + -4X2)) = 0 Combine like terms: 6X + -8X = -2X (12 + -2X + -4X2) = 0 Solving 12 + -2X + -4X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -1X + -2X2) = 0 Factor a trinomial. 2((3 + -2X)(2 + X)) = 0 Ignore the factor 2.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 '(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 = -2Solution
X = {1.5, -2}
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