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Simplifying (x + 7)(x + 3) = x + 10x + 21 Reorder the terms: (7 + x)(x + 3) = x + 10x + 21 Reorder the terms: (7 + x)(3 + x) = x + 10x + 21 Multiply (7 + x) * (3 + x) (7(3 + x) + x(3 + x)) = x + 10x + 21 ((3 * 7 + x * 7) + x(3 + x)) = x + 10x + 21 ((21 + 7x) + x(3 + x)) = x + 10x + 21 (21 + 7x + (3 * x + x * x)) = x + 10x + 21 (21 + 7x + (3x + x2)) = x + 10x + 21 Combine like terms: 7x + 3x = 10x (21 + 10x + x2) = x + 10x + 21 Reorder the terms: 21 + 10x + x2 = 21 + x + 10x Combine like terms: x + 10x = 11x 21 + 10x + x2 = 21 + 11x Add '-21' to each side of the equation. 21 + 10x + -21 + x2 = 21 + -21 + 11x Reorder the terms: 21 + -21 + 10x + x2 = 21 + -21 + 11x Combine like terms: 21 + -21 = 0 0 + 10x + x2 = 21 + -21 + 11x 10x + x2 = 21 + -21 + 11x Combine like terms: 21 + -21 = 0 10x + x2 = 0 + 11x 10x + x2 = 11x Solving 10x + x2 = 11x Solving for variable 'x'. Reorder the terms: 10x + -11x + x2 = 11x + -11x Combine like terms: 10x + -11x = -1x -1x + x2 = 11x + -11x Combine like terms: 11x + -11x = 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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