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Simplifying (x + 1)(3x + 1) = x + x + 1 + 96 Reorder the terms: (1 + x)(3x + 1) = x + x + 1 + 96 Reorder the terms: (1 + x)(1 + 3x) = x + x + 1 + 96 Multiply (1 + x) * (1 + 3x) (1(1 + 3x) + x(1 + 3x)) = x + x + 1 + 96 ((1 * 1 + 3x * 1) + x(1 + 3x)) = x + x + 1 + 96 ((1 + 3x) + x(1 + 3x)) = x + x + 1 + 96 (1 + 3x + (1 * x + 3x * x)) = x + x + 1 + 96 (1 + 3x + (1x + 3x2)) = x + x + 1 + 96 Combine like terms: 3x + 1x = 4x (1 + 4x + 3x2) = x + x + 1 + 96 Reorder the terms: 1 + 4x + 3x2 = 1 + 96 + x + x Combine like terms: 1 + 96 = 97 1 + 4x + 3x2 = 97 + x + x Combine like terms: x + x = 2x 1 + 4x + 3x2 = 97 + 2x Solving 1 + 4x + 3x2 = 97 + 2x Solving for variable 'x'. Reorder the terms: 1 + -97 + 4x + -2x + 3x2 = 97 + 2x + -97 + -2x Combine like terms: 1 + -97 = -96 -96 + 4x + -2x + 3x2 = 97 + 2x + -97 + -2x Combine like terms: 4x + -2x = 2x -96 + 2x + 3x2 = 97 + 2x + -97 + -2x Reorder the terms: -96 + 2x + 3x2 = 97 + -97 + 2x + -2x Combine like terms: 97 + -97 = 0 -96 + 2x + 3x2 = 0 + 2x + -2x -96 + 2x + 3x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -96 + 2x + 3x2 = 0 Factor a trinomial. (-6 + -1x)(16 + -3x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(16 + -3x)' equal to zero and attempt to solve: Simplifying 16 + -3x = 0 Solving 16 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -3x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -3x = 0 + -16 -3x = 0 + -16 Combine like terms: 0 + -16 = -16 -3x = -16 Divide each side by '-3'. x = 5.333333333 Simplifying x = 5.333333333Solution
x = {-6, 5.333333333}
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