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Simplifying 75x3 = 48x Solving 75x3 = 48x Solving for variable 'x'. Reorder the terms: -48x + 75x3 = 48x + -48x Combine like terms: 48x + -48x = 0 -48x + 75x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-16 + 25x2) = 0 Factor a difference between two squares. 3x((4 + 5x)(-4 + 5x)) = 0 Ignore the factor 3.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 '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Divide each side by '5'. x = -0.8 Simplifying x = -0.8Subproblem 3
Set the factor '(-4 + 5x)' equal to zero and attempt to solve: Simplifying -4 + 5x = 0 Solving -4 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5x = 0 + 4 5x = 0 + 4 Combine like terms: 0 + 4 = 4 5x = 4 Divide each side by '5'. x = 0.8 Simplifying x = 0.8Solution
x = {0, -0.8, 0.8}
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