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Simplifying 2x + 3x2 = 4x + -5x2 Solving 2x + 3x2 = 4x + -5x2 Solving for variable 'x'. Reorder the terms: 2x + -4x + 3x2 + 5x2 = 4x + -5x2 + -4x + 5x2 Combine like terms: 2x + -4x = -2x -2x + 3x2 + 5x2 = 4x + -5x2 + -4x + 5x2 Combine like terms: 3x2 + 5x2 = 8x2 -2x + 8x2 = 4x + -5x2 + -4x + 5x2 Reorder the terms: -2x + 8x2 = 4x + -4x + -5x2 + 5x2 Combine like terms: 4x + -4x = 0 -2x + 8x2 = 0 + -5x2 + 5x2 -2x + 8x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -2x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + 4x) = 0 Ignore the factor 2.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 '(-1 + 4x)' equal to zero and attempt to solve: Simplifying -1 + 4x = 0 Solving -1 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 0 + 1 4x = 0 + 1 Combine like terms: 0 + 1 = 1 4x = 1 Divide each side by '4'. x = 0.25 Simplifying x = 0.25Solution
x = {0, 0.25}
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