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Simplifying 14x2 + -5x = 3x + -10x2 Reorder the terms: -5x + 14x2 = 3x + -10x2 Solving -5x + 14x2 = 3x + -10x2 Solving for variable 'x'. Reorder the terms: -5x + -3x + 14x2 + 10x2 = 3x + -10x2 + -3x + 10x2 Combine like terms: -5x + -3x = -8x -8x + 14x2 + 10x2 = 3x + -10x2 + -3x + 10x2 Combine like terms: 14x2 + 10x2 = 24x2 -8x + 24x2 = 3x + -10x2 + -3x + 10x2 Reorder the terms: -8x + 24x2 = 3x + -3x + -10x2 + 10x2 Combine like terms: 3x + -3x = 0 -8x + 24x2 = 0 + -10x2 + 10x2 -8x + 24x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -8x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '8x'. 8x(-1 + 3x) = 0 Ignore the factor 8.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 + 3x)' equal to zero and attempt to solve: Simplifying -1 + 3x = 0 Solving -1 + 3x = 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 + 3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x = 0 + 1 3x = 0 + 1 Combine like terms: 0 + 1 = 1 3x = 1 Divide each side by '3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {0, 0.3333333333}
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