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Simplifying 3x(x + 7) = 4x(2x + -1) Reorder the terms: 3x(7 + x) = 4x(2x + -1) (7 * 3x + x * 3x) = 4x(2x + -1) (21x + 3x2) = 4x(2x + -1) Reorder the terms: 21x + 3x2 = 4x(-1 + 2x) 21x + 3x2 = (-1 * 4x + 2x * 4x) 21x + 3x2 = (-4x + 8x2) Solving 21x + 3x2 = -4x + 8x2 Solving for variable 'x'. Reorder the terms: 21x + 4x + 3x2 + -8x2 = -4x + 8x2 + 4x + -8x2 Combine like terms: 21x + 4x = 25x 25x + 3x2 + -8x2 = -4x + 8x2 + 4x + -8x2 Combine like terms: 3x2 + -8x2 = -5x2 25x + -5x2 = -4x + 8x2 + 4x + -8x2 Reorder the terms: 25x + -5x2 = -4x + 4x + 8x2 + -8x2 Combine like terms: -4x + 4x = 0 25x + -5x2 = 0 + 8x2 + -8x2 25x + -5x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 25x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, 5}
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