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Simplifying (2x + 7)(6x + 7) = 13x + 14 Reorder the terms: (7 + 2x)(6x + 7) = 13x + 14 Reorder the terms: (7 + 2x)(7 + 6x) = 13x + 14 Multiply (7 + 2x) * (7 + 6x) (7(7 + 6x) + 2x * (7 + 6x)) = 13x + 14 ((7 * 7 + 6x * 7) + 2x * (7 + 6x)) = 13x + 14 ((49 + 42x) + 2x * (7 + 6x)) = 13x + 14 (49 + 42x + (7 * 2x + 6x * 2x)) = 13x + 14 (49 + 42x + (14x + 12x2)) = 13x + 14 Combine like terms: 42x + 14x = 56x (49 + 56x + 12x2) = 13x + 14 Reorder the terms: 49 + 56x + 12x2 = 14 + 13x Solving 49 + 56x + 12x2 = 14 + 13x Solving for variable 'x'. Reorder the terms: 49 + -14 + 56x + -13x + 12x2 = 14 + 13x + -14 + -13x Combine like terms: 49 + -14 = 35 35 + 56x + -13x + 12x2 = 14 + 13x + -14 + -13x Combine like terms: 56x + -13x = 43x 35 + 43x + 12x2 = 14 + 13x + -14 + -13x Reorder the terms: 35 + 43x + 12x2 = 14 + -14 + 13x + -13x Combine like terms: 14 + -14 = 0 35 + 43x + 12x2 = 0 + 13x + -13x 35 + 43x + 12x2 = 13x + -13x Combine like terms: 13x + -13x = 0 35 + 43x + 12x2 = 0 Factor a trinomial. (7 + 3x)(5 + 4x) = 0Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25Solution
x = {-2.333333333, -1.25}
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