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Simplifying (3x + -1)(x + 4) = 13x + 1 Reorder the terms: (-1 + 3x)(x + 4) = 13x + 1 Reorder the terms: (-1 + 3x)(4 + x) = 13x + 1 Multiply (-1 + 3x) * (4 + x) (-1(4 + x) + 3x * (4 + x)) = 13x + 1 ((4 * -1 + x * -1) + 3x * (4 + x)) = 13x + 1 ((-4 + -1x) + 3x * (4 + x)) = 13x + 1 (-4 + -1x + (4 * 3x + x * 3x)) = 13x + 1 (-4 + -1x + (12x + 3x2)) = 13x + 1 Combine like terms: -1x + 12x = 11x (-4 + 11x + 3x2) = 13x + 1 Reorder the terms: -4 + 11x + 3x2 = 1 + 13x Solving -4 + 11x + 3x2 = 1 + 13x Solving for variable 'x'. Reorder the terms: -4 + -1 + 11x + -13x + 3x2 = 1 + 13x + -1 + -13x Combine like terms: -4 + -1 = -5 -5 + 11x + -13x + 3x2 = 1 + 13x + -1 + -13x Combine like terms: 11x + -13x = -2x -5 + -2x + 3x2 = 1 + 13x + -1 + -13x Reorder the terms: -5 + -2x + 3x2 = 1 + -1 + 13x + -13x Combine like terms: 1 + -1 = 0 -5 + -2x + 3x2 = 0 + 13x + -13x -5 + -2x + 3x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -5 + -2x + 3x2 = 0 Factor a trinomial. (-1 + -1x)(5 + -3x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {-1, 1.666666667}
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