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Simplifying (3x + -1)(x + 3) + -1(x + 2) = 1 Reorder the terms: (-1 + 3x)(x + 3) + -1(x + 2) = 1 Reorder the terms: (-1 + 3x)(3 + x) + -1(x + 2) = 1 Multiply (-1 + 3x) * (3 + x) (-1(3 + x) + 3x * (3 + x)) + -1(x + 2) = 1 ((3 * -1 + x * -1) + 3x * (3 + x)) + -1(x + 2) = 1 ((-3 + -1x) + 3x * (3 + x)) + -1(x + 2) = 1 (-3 + -1x + (3 * 3x + x * 3x)) + -1(x + 2) = 1 (-3 + -1x + (9x + 3x2)) + -1(x + 2) = 1 Combine like terms: -1x + 9x = 8x (-3 + 8x + 3x2) + -1(x + 2) = 1 Reorder the terms: -3 + 8x + 3x2 + -1(2 + x) = 1 -3 + 8x + 3x2 + (2 * -1 + x * -1) = 1 -3 + 8x + 3x2 + (-2 + -1x) = 1 Reorder the terms: -3 + -2 + 8x + -1x + 3x2 = 1 Combine like terms: -3 + -2 = -5 -5 + 8x + -1x + 3x2 = 1 Combine like terms: 8x + -1x = 7x -5 + 7x + 3x2 = 1 Solving -5 + 7x + 3x2 = 1 Solving for variable 'x'. Reorder the terms: -5 + -1 + 7x + 3x2 = 1 + -1 Combine like terms: -5 + -1 = -6 -6 + 7x + 3x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -6 + 7x + 3x2 = 0 Factor a trinomial. (-3 + -1x)(2 + -3x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-3, 0.6666666667}
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