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Simplifying (2X + 5)(4X + -2) = 0 Reorder the terms: (5 + 2X)(4X + -2) = 0 Reorder the terms: (5 + 2X)(-2 + 4X) = 0 Multiply (5 + 2X) * (-2 + 4X) (5(-2 + 4X) + 2X * (-2 + 4X)) = 0 ((-2 * 5 + 4X * 5) + 2X * (-2 + 4X)) = 0 ((-10 + 20X) + 2X * (-2 + 4X)) = 0 (-10 + 20X + (-2 * 2X + 4X * 2X)) = 0 (-10 + 20X + (-4X + 8X2)) = 0 Combine like terms: 20X + -4X = 16X (-10 + 16X + 8X2) = 0 Solving -10 + 16X + 8X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 8X + 4X2) = 0 Factor a trinomial. 2((-5 + -2X)(1 + -2X)) = 0 Ignore the factor 2.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 + -2X)' equal to zero and attempt to solve: Simplifying 1 + -2X = 0 Solving 1 + -2X = 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 + -2X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2X = 0 + -1 -2X = 0 + -1 Combine like terms: 0 + -1 = -1 -2X = -1 Divide each side by '-2'. X = 0.5 Simplifying X = 0.5Solution
X = {-2.5, 0.5}
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