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