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Simplifying (3x + 2)(x + 3) = x + 14 Reorder the terms: (2 + 3x)(x + 3) = x + 14 Reorder the terms: (2 + 3x)(3 + x) = x + 14 Multiply (2 + 3x) * (3 + x) (2(3 + x) + 3x * (3 + x)) = x + 14 ((3 * 2 + x * 2) + 3x * (3 + x)) = x + 14 ((6 + 2x) + 3x * (3 + x)) = x + 14 (6 + 2x + (3 * 3x + x * 3x)) = x + 14 (6 + 2x + (9x + 3x2)) = x + 14 Combine like terms: 2x + 9x = 11x (6 + 11x + 3x2) = x + 14 Reorder the terms: 6 + 11x + 3x2 = 14 + x Solving 6 + 11x + 3x2 = 14 + x Solving for variable 'x'. Reorder the terms: 6 + -14 + 11x + -1x + 3x2 = 14 + x + -14 + -1x Combine like terms: 6 + -14 = -8 -8 + 11x + -1x + 3x2 = 14 + x + -14 + -1x Combine like terms: 11x + -1x = 10x -8 + 10x + 3x2 = 14 + x + -14 + -1x Reorder the terms: -8 + 10x + 3x2 = 14 + -14 + x + -1x Combine like terms: 14 + -14 = 0 -8 + 10x + 3x2 = 0 + x + -1x -8 + 10x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -8 + 10x + 3x2 = 0 Factor a trinomial. (-4 + -1x)(2 + -3x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 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 = {-4, 0.6666666667}
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