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Simplifying 3x(x + -2) = 5x2 + -7x Reorder the terms: 3x(-2 + x) = 5x2 + -7x (-2 * 3x + x * 3x) = 5x2 + -7x (-6x + 3x2) = 5x2 + -7x Reorder the terms: -6x + 3x2 = -7x + 5x2 Solving -6x + 3x2 = -7x + 5x2 Solving for variable 'x'. Reorder the terms: -6x + 7x + 3x2 + -5x2 = -7x + 5x2 + 7x + -5x2 Combine like terms: -6x + 7x = 1x 1x + 3x2 + -5x2 = -7x + 5x2 + 7x + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 1x + -2x2 = -7x + 5x2 + 7x + -5x2 Reorder the terms: 1x + -2x2 = -7x + 7x + 5x2 + -5x2 Combine like terms: -7x + 7x = 0 1x + -2x2 = 0 + 5x2 + -5x2 1x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 1x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -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 '(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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