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Simplifying (2 + 4x)(-5 + x) = 0 Multiply (2 + 4x) * (-5 + x) (2(-5 + x) + 4x * (-5 + x)) = 0 ((-5 * 2 + x * 2) + 4x * (-5 + x)) = 0 ((-10 + 2x) + 4x * (-5 + x)) = 0 (-10 + 2x + (-5 * 4x + x * 4x)) = 0 (-10 + 2x + (-20x + 4x2)) = 0 Combine like terms: 2x + -20x = -18x (-10 + -18x + 4x2) = 0 Solving -10 + -18x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -9x + 2x2) = 0 Factor a trinomial. 2((-1 + -2x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-0.5, 5}
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