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Simplifying (4x + -5)(2x + -10) = 0 Reorder the terms: (-5 + 4x)(2x + -10) = 0 Reorder the terms: (-5 + 4x)(-10 + 2x) = 0 Multiply (-5 + 4x) * (-10 + 2x) (-5(-10 + 2x) + 4x * (-10 + 2x)) = 0 ((-10 * -5 + 2x * -5) + 4x * (-10 + 2x)) = 0 ((50 + -10x) + 4x * (-10 + 2x)) = 0 (50 + -10x + (-10 * 4x + 2x * 4x)) = 0 (50 + -10x + (-40x + 8x2)) = 0 Combine like terms: -10x + -40x = -50x (50 + -50x + 8x2) = 0 Solving 50 + -50x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -25x + 4x2) = 0 Factor a trinomial. 2((5 + -4x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Subproblem 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 = {1.25, 5}
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