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Simplifying (-1x + -3)(-1x + -2) = (-1x + 5)(-2x + -3) + 21 Reorder the terms: (-3 + -1x)(-1x + -2) = (-1x + 5)(-2x + -3) + 21 Reorder the terms: (-3 + -1x)(-2 + -1x) = (-1x + 5)(-2x + -3) + 21 Multiply (-3 + -1x) * (-2 + -1x) (-3(-2 + -1x) + -1x * (-2 + -1x)) = (-1x + 5)(-2x + -3) + 21 ((-2 * -3 + -1x * -3) + -1x * (-2 + -1x)) = (-1x + 5)(-2x + -3) + 21 ((6 + 3x) + -1x * (-2 + -1x)) = (-1x + 5)(-2x + -3) + 21 (6 + 3x + (-2 * -1x + -1x * -1x)) = (-1x + 5)(-2x + -3) + 21 (6 + 3x + (2x + 1x2)) = (-1x + 5)(-2x + -3) + 21 Combine like terms: 3x + 2x = 5x (6 + 5x + 1x2) = (-1x + 5)(-2x + -3) + 21 Reorder the terms: 6 + 5x + 1x2 = (5 + -1x)(-2x + -3) + 21 Reorder the terms: 6 + 5x + 1x2 = (5 + -1x)(-3 + -2x) + 21 Multiply (5 + -1x) * (-3 + -2x) 6 + 5x + 1x2 = (5(-3 + -2x) + -1x * (-3 + -2x)) + 21 6 + 5x + 1x2 = ((-3 * 5 + -2x * 5) + -1x * (-3 + -2x)) + 21 6 + 5x + 1x2 = ((-15 + -10x) + -1x * (-3 + -2x)) + 21 6 + 5x + 1x2 = (-15 + -10x + (-3 * -1x + -2x * -1x)) + 21 6 + 5x + 1x2 = (-15 + -10x + (3x + 2x2)) + 21 Combine like terms: -10x + 3x = -7x 6 + 5x + 1x2 = (-15 + -7x + 2x2) + 21 Reorder the terms: 6 + 5x + 1x2 = -15 + 21 + -7x + 2x2 Combine like terms: -15 + 21 = 6 6 + 5x + 1x2 = 6 + -7x + 2x2 Add '-6' to each side of the equation. 6 + 5x + -6 + 1x2 = 6 + -7x + -6 + 2x2 Reorder the terms: 6 + -6 + 5x + 1x2 = 6 + -7x + -6 + 2x2 Combine like terms: 6 + -6 = 0 0 + 5x + 1x2 = 6 + -7x + -6 + 2x2 5x + 1x2 = 6 + -7x + -6 + 2x2 Reorder the terms: 5x + 1x2 = 6 + -6 + -7x + 2x2 Combine like terms: 6 + -6 = 0 5x + 1x2 = 0 + -7x + 2x2 5x + 1x2 = -7x + 2x2 Solving 5x + 1x2 = -7x + 2x2 Solving for variable 'x'. Reorder the terms: 5x + 7x + 1x2 + -2x2 = -7x + 2x2 + 7x + -2x2 Combine like terms: 5x + 7x = 12x 12x + 1x2 + -2x2 = -7x + 2x2 + 7x + -2x2 Combine like terms: 1x2 + -2x2 = -1x2 12x + -1x2 = -7x + 2x2 + 7x + -2x2 Reorder the terms: 12x + -1x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 12x + -1x2 = 0 + 2x2 + -2x2 12x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(12 + -1x) = 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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {0, 12}
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