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Simplifying 0 = -2x2 + 3x + 0 Reorder the terms: 0 = 0 + 3x + -2x2 Remove the zero: 0 = 3x + -2x2 Solving 0 = 3x + -2x2 Solving for variable 'x'. Remove the zero: -3x + 2x2 = 3x + -2x2 + -3x + 2x2 Reorder the terms: -3x + 2x2 = 3x + -3x + -2x2 + 2x2 Combine like terms: 3x + -3x = 0 -3x + 2x2 = 0 + -2x2 + 2x2 -3x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -3x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + 2x) = 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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5}
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