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Simplifying 2x(5x + -1) = 3x(2x + 1) Reorder the terms: 2x(-1 + 5x) = 3x(2x + 1) (-1 * 2x + 5x * 2x) = 3x(2x + 1) (-2x + 10x2) = 3x(2x + 1) Reorder the terms: -2x + 10x2 = 3x(1 + 2x) -2x + 10x2 = (1 * 3x + 2x * 3x) -2x + 10x2 = (3x + 6x2) Solving -2x + 10x2 = 3x + 6x2 Solving for variable 'x'. Reorder the terms: -2x + -3x + 10x2 + -6x2 = 3x + 6x2 + -3x + -6x2 Combine like terms: -2x + -3x = -5x -5x + 10x2 + -6x2 = 3x + 6x2 + -3x + -6x2 Combine like terms: 10x2 + -6x2 = 4x2 -5x + 4x2 = 3x + 6x2 + -3x + -6x2 Reorder the terms: -5x + 4x2 = 3x + -3x + 6x2 + -6x2 Combine like terms: 3x + -3x = 0 -5x + 4x2 = 0 + 6x2 + -6x2 -5x + 4x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -5x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 4x) = 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 '(-5 + 4x)' equal to zero and attempt to solve: Simplifying -5 + 4x = 0 Solving -5 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x = 0 + 5 4x = 0 + 5 Combine like terms: 0 + 5 = 5 4x = 5 Divide each side by '4'. x = 1.25 Simplifying x = 1.25Solution
x = {0, 1.25}
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