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Simplifying 96 = (x + 1)(3x + 1) Reorder the terms: 96 = (1 + x)(3x + 1) Reorder the terms: 96 = (1 + x)(1 + 3x) Multiply (1 + x) * (1 + 3x) 96 = (1(1 + 3x) + x(1 + 3x)) 96 = ((1 * 1 + 3x * 1) + x(1 + 3x)) 96 = ((1 + 3x) + x(1 + 3x)) 96 = (1 + 3x + (1 * x + 3x * x)) 96 = (1 + 3x + (1x + 3x2)) Combine like terms: 3x + 1x = 4x 96 = (1 + 4x + 3x2) Solving 96 = 1 + 4x + 3x2 Solving for variable 'x'. Combine like terms: 96 + -1 = 95 95 + -4x + -3x2 = 1 + 4x + 3x2 + -1 + -4x + -3x2 Reorder the terms: 95 + -4x + -3x2 = 1 + -1 + 4x + -4x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 95 + -4x + -3x2 = 0 + 4x + -4x + 3x2 + -3x2 95 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 95 + -4x + -3x2 = 0 + 3x2 + -3x2 95 + -4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 95 + -4x + -3x2 = 0 Factor a trinomial. (5 + -1x)(19 + 3x) = 0Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(19 + 3x)' equal to zero and attempt to solve: Simplifying 19 + 3x = 0 Solving 19 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 3x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 3x = 0 + -19 3x = 0 + -19 Combine like terms: 0 + -19 = -19 3x = -19 Divide each side by '3'. x = -6.333333333 Simplifying x = -6.333333333Solution
x = {5, -6.333333333}
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