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Simplifying 8x2 + -6x = 4x + -12x2 Reorder the terms: -6x + 8x2 = 4x + -12x2 Solving -6x + 8x2 = 4x + -12x2 Solving for variable 'x'. Reorder the terms: -6x + -4x + 8x2 + 12x2 = 4x + -12x2 + -4x + 12x2 Combine like terms: -6x + -4x = -10x -10x + 8x2 + 12x2 = 4x + -12x2 + -4x + 12x2 Combine like terms: 8x2 + 12x2 = 20x2 -10x + 20x2 = 4x + -12x2 + -4x + 12x2 Reorder the terms: -10x + 20x2 = 4x + -4x + -12x2 + 12x2 Combine like terms: 4x + -4x = 0 -10x + 20x2 = 0 + -12x2 + 12x2 -10x + 20x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -10x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '10x'. 10x(-1 + 2x) = 0 Ignore the factor 10.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 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5Solution
x = {0, 0.5}
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