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Simplifying 600x = 800x(x + -0.75) Reorder the terms: 600x = 800x(-0.75 + x) 600x = (-0.75 * 800x + x * 800x) 600x = (-600x + 800x2) Solving 600x = -600x + 800x2 Solving for variable 'x'. Combine like terms: 600x + 600x = 1200x 1200x + -800x2 = -600x + 800x2 + 600x + -800x2 Reorder the terms: 1200x + -800x2 = -600x + 600x + 800x2 + -800x2 Combine like terms: -600x + 600x = 0 1200x + -800x2 = 0 + 800x2 + -800x2 1200x + -800x2 = 800x2 + -800x2 Combine like terms: 800x2 + -800x2 = 0 1200x + -800x2 = 0 Factor out the Greatest Common Factor (GCF), '400x'. 400x(3 + -2x) = 0 Ignore the factor 400.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = {0, 1.5}
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