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Simplifying 4x(6x + -10) = 5x(4x + 8) Reorder the terms: 4x(-10 + 6x) = 5x(4x + 8) (-10 * 4x + 6x * 4x) = 5x(4x + 8) (-40x + 24x2) = 5x(4x + 8) Reorder the terms: -40x + 24x2 = 5x(8 + 4x) -40x + 24x2 = (8 * 5x + 4x * 5x) -40x + 24x2 = (40x + 20x2) Solving -40x + 24x2 = 40x + 20x2 Solving for variable 'x'. Reorder the terms: -40x + -40x + 24x2 + -20x2 = 40x + 20x2 + -40x + -20x2 Combine like terms: -40x + -40x = -80x -80x + 24x2 + -20x2 = 40x + 20x2 + -40x + -20x2 Combine like terms: 24x2 + -20x2 = 4x2 -80x + 4x2 = 40x + 20x2 + -40x + -20x2 Reorder the terms: -80x + 4x2 = 40x + -40x + 20x2 + -20x2 Combine like terms: 40x + -40x = 0 -80x + 4x2 = 0 + 20x2 + -20x2 -80x + 4x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-20 + x) = 0 Ignore the factor 4.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 '(-20 + x)' equal to zero and attempt to solve: Simplifying -20 + x = 0 Solving -20 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + x = 0 + 20 x = 0 + 20 Combine like terms: 0 + 20 = 20 x = 20 Simplifying x = 20Solution
x = {0, 20}
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