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Simplifying (x + -1)(27x + 2) = 5x + 23 Reorder the terms: (-1 + x)(27x + 2) = 5x + 23 Reorder the terms: (-1 + x)(2 + 27x) = 5x + 23 Multiply (-1 + x) * (2 + 27x) (-1(2 + 27x) + x(2 + 27x)) = 5x + 23 ((2 * -1 + 27x * -1) + x(2 + 27x)) = 5x + 23 ((-2 + -27x) + x(2 + 27x)) = 5x + 23 (-2 + -27x + (2 * x + 27x * x)) = 5x + 23 (-2 + -27x + (2x + 27x2)) = 5x + 23 Combine like terms: -27x + 2x = -25x (-2 + -25x + 27x2) = 5x + 23 Reorder the terms: -2 + -25x + 27x2 = 23 + 5x Solving -2 + -25x + 27x2 = 23 + 5x Solving for variable 'x'. Reorder the terms: -2 + -23 + -25x + -5x + 27x2 = 23 + 5x + -23 + -5x Combine like terms: -2 + -23 = -25 -25 + -25x + -5x + 27x2 = 23 + 5x + -23 + -5x Combine like terms: -25x + -5x = -30x -25 + -30x + 27x2 = 23 + 5x + -23 + -5x Reorder the terms: -25 + -30x + 27x2 = 23 + -23 + 5x + -5x Combine like terms: 23 + -23 = 0 -25 + -30x + 27x2 = 0 + 5x + -5x -25 + -30x + 27x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -25 + -30x + 27x2 = 0 Factor a trinomial. (-5 + -9x)(5 + -3x) = 0Subproblem 1
Set the factor '(-5 + -9x)' equal to zero and attempt to solve: Simplifying -5 + -9x = 0 Solving -5 + -9x = 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 + -9x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -9x = 0 + 5 -9x = 0 + 5 Combine like terms: 0 + 5 = 5 -9x = 5 Divide each side by '-9'. x = -0.5555555556 Simplifying x = -0.5555555556Subproblem 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 = {-0.5555555556, 1.666666667}
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