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Simplifying 6 = -5x2 + 10x + 6 Reorder the terms: 6 = 6 + 10x + -5x2 Add '-6' to each side of the equation. 6 + -6 = 6 + 10x + -6 + -5x2 Combine like terms: 6 + -6 = 0 0 = 6 + 10x + -6 + -5x2 Reorder the terms: 0 = 6 + -6 + 10x + -5x2 Combine like terms: 6 + -6 = 0 0 = 0 + 10x + -5x2 0 = 10x + -5x2 Solving 0 = 10x + -5x2 Solving for variable 'x'. Remove the zero: -10x + 5x2 = 10x + -5x2 + -10x + 5x2 Reorder the terms: -10x + 5x2 = 10x + -10x + -5x2 + 5x2 Combine like terms: 10x + -10x = 0 -10x + 5x2 = 0 + -5x2 + 5x2 -10x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-2 + x) = 0 Ignore the factor 5.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {0, 2}
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