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Simplifying 14(x + 1) = (3x + -1)(2x + 1) Reorder the terms: 14(1 + x) = (3x + -1)(2x + 1) (1 * 14 + x * 14) = (3x + -1)(2x + 1) (14 + 14x) = (3x + -1)(2x + 1) Reorder the terms: 14 + 14x = (-1 + 3x)(2x + 1) Reorder the terms: 14 + 14x = (-1 + 3x)(1 + 2x) Multiply (-1 + 3x) * (1 + 2x) 14 + 14x = (-1(1 + 2x) + 3x * (1 + 2x)) 14 + 14x = ((1 * -1 + 2x * -1) + 3x * (1 + 2x)) 14 + 14x = ((-1 + -2x) + 3x * (1 + 2x)) 14 + 14x = (-1 + -2x + (1 * 3x + 2x * 3x)) 14 + 14x = (-1 + -2x + (3x + 6x2)) Combine like terms: -2x + 3x = 1x 14 + 14x = (-1 + 1x + 6x2) Solving 14 + 14x = -1 + 1x + 6x2 Solving for variable 'x'. Reorder the terms: 14 + 1 + 14x + -1x + -6x2 = -1 + 1x + 6x2 + 1 + -1x + -6x2 Combine like terms: 14 + 1 = 15 15 + 14x + -1x + -6x2 = -1 + 1x + 6x2 + 1 + -1x + -6x2 Combine like terms: 14x + -1x = 13x 15 + 13x + -6x2 = -1 + 1x + 6x2 + 1 + -1x + -6x2 Reorder the terms: 15 + 13x + -6x2 = -1 + 1 + 1x + -1x + 6x2 + -6x2 Combine like terms: -1 + 1 = 0 15 + 13x + -6x2 = 0 + 1x + -1x + 6x2 + -6x2 15 + 13x + -6x2 = 1x + -1x + 6x2 + -6x2 Combine like terms: 1x + -1x = 0 15 + 13x + -6x2 = 0 + 6x2 + -6x2 15 + 13x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 15 + 13x + -6x2 = 0 Factor a trinomial. (3 + -1x)(5 + 6x) = 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 '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Divide each side by '6'. x = -0.8333333333 Simplifying x = -0.8333333333Solution
x = {3, -0.8333333333}
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