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Simplifying (x + 3)(x + 1) = -10x + 18 Reorder the terms: (3 + x)(x + 1) = -10x + 18 Reorder the terms: (3 + x)(1 + x) = -10x + 18 Multiply (3 + x) * (1 + x) (3(1 + x) + x(1 + x)) = -10x + 18 ((1 * 3 + x * 3) + x(1 + x)) = -10x + 18 ((3 + 3x) + x(1 + x)) = -10x + 18 (3 + 3x + (1 * x + x * x)) = -10x + 18 (3 + 3x + (1x + x2)) = -10x + 18 Combine like terms: 3x + 1x = 4x (3 + 4x + x2) = -10x + 18 Reorder the terms: 3 + 4x + x2 = 18 + -10x Solving 3 + 4x + x2 = 18 + -10x Solving for variable 'x'. Reorder the terms: 3 + -18 + 4x + 10x + x2 = 18 + -10x + -18 + 10x Combine like terms: 3 + -18 = -15 -15 + 4x + 10x + x2 = 18 + -10x + -18 + 10x Combine like terms: 4x + 10x = 14x -15 + 14x + x2 = 18 + -10x + -18 + 10x Reorder the terms: -15 + 14x + x2 = 18 + -18 + -10x + 10x Combine like terms: 18 + -18 = 0 -15 + 14x + x2 = 0 + -10x + 10x -15 + 14x + x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -15 + 14x + x2 = 0 Factor a trinomial. (-15 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-15, 1}
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