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Simplifying (x + 3)(x + -2) = 13x + -17 Reorder the terms: (3 + x)(x + -2) = 13x + -17 Reorder the terms: (3 + x)(-2 + x) = 13x + -17 Multiply (3 + x) * (-2 + x) (3(-2 + x) + x(-2 + x)) = 13x + -17 ((-2 * 3 + x * 3) + x(-2 + x)) = 13x + -17 ((-6 + 3x) + x(-2 + x)) = 13x + -17 (-6 + 3x + (-2 * x + x * x)) = 13x + -17 (-6 + 3x + (-2x + x2)) = 13x + -17 Combine like terms: 3x + -2x = 1x (-6 + 1x + x2) = 13x + -17 Reorder the terms: -6 + 1x + x2 = -17 + 13x Solving -6 + 1x + x2 = -17 + 13x Solving for variable 'x'. Reorder the terms: -6 + 17 + 1x + -13x + x2 = -17 + 13x + 17 + -13x Combine like terms: -6 + 17 = 11 11 + 1x + -13x + x2 = -17 + 13x + 17 + -13x Combine like terms: 1x + -13x = -12x 11 + -12x + x2 = -17 + 13x + 17 + -13x Reorder the terms: 11 + -12x + x2 = -17 + 17 + 13x + -13x Combine like terms: -17 + 17 = 0 11 + -12x + x2 = 0 + 13x + -13x 11 + -12x + x2 = 13x + -13x Combine like terms: 13x + -13x = 0 11 + -12x + x2 = 0 Factor a trinomial. (1 + -1x)(11 + -1x) = 0Subproblem 1
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 = 1Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Solution
x = {1, 11}
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