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Simplifying 5x2 + 3x = 2x2 + 5x Reorder the terms: 3x + 5x2 = 2x2 + 5x Reorder the terms: 3x + 5x2 = 5x + 2x2 Solving 3x + 5x2 = 5x + 2x2 Solving for variable 'x'. Reorder the terms: 3x + -5x + 5x2 + -2x2 = 5x + 2x2 + -5x + -2x2 Combine like terms: 3x + -5x = -2x -2x + 5x2 + -2x2 = 5x + 2x2 + -5x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -2x + 3x2 = 5x + 2x2 + -5x + -2x2 Reorder the terms: -2x + 3x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 -2x + 3x2 = 0 + 2x2 + -2x2 -2x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -2x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + 3x) = 0Subproblem 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 '(-2 + 3x)' equal to zero and attempt to solve: Simplifying -2 + 3x = 0 Solving -2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x = 0 + 2 3x = 0 + 2 Combine like terms: 0 + 2 = 2 3x = 2 Divide each side by '3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {0, 0.6666666667}
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