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Simplifying 65 = (3x + 1)(x + 1) Reorder the terms: 65 = (1 + 3x)(x + 1) Reorder the terms: 65 = (1 + 3x)(1 + x) Multiply (1 + 3x) * (1 + x) 65 = (1(1 + x) + 3x * (1 + x)) 65 = ((1 * 1 + x * 1) + 3x * (1 + x)) 65 = ((1 + 1x) + 3x * (1 + x)) 65 = (1 + 1x + (1 * 3x + x * 3x)) 65 = (1 + 1x + (3x + 3x2)) Combine like terms: 1x + 3x = 4x 65 = (1 + 4x + 3x2) Solving 65 = 1 + 4x + 3x2 Solving for variable 'x'. Combine like terms: 65 + -1 = 64 64 + -4x + -3x2 = 1 + 4x + 3x2 + -1 + -4x + -3x2 Reorder the terms: 64 + -4x + -3x2 = 1 + -1 + 4x + -4x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 64 + -4x + -3x2 = 0 + 4x + -4x + 3x2 + -3x2 64 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 64 + -4x + -3x2 = 0 + 3x2 + -3x2 64 + -4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 64 + -4x + -3x2 = 0 Factor a trinomial. (4 + -1x)(16 + 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 '(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 = {4, -5.333333333}
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