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