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Simplifying (5x + -1)(x + 1) + -5 + x = -5 + x Reorder the terms: (-1 + 5x)(x + 1) + -5 + x = -5 + x Reorder the terms: (-1 + 5x)(1 + x) + -5 + x = -5 + x Multiply (-1 + 5x) * (1 + x) (-1(1 + x) + 5x * (1 + x)) + -5 + x = -5 + x ((1 * -1 + x * -1) + 5x * (1 + x)) + -5 + x = -5 + x ((-1 + -1x) + 5x * (1 + x)) + -5 + x = -5 + x (-1 + -1x + (1 * 5x + x * 5x)) + -5 + x = -5 + x (-1 + -1x + (5x + 5x2)) + -5 + x = -5 + x Combine like terms: -1x + 5x = 4x (-1 + 4x + 5x2) + -5 + x = -5 + x Reorder the terms: -1 + -5 + 4x + x + 5x2 = -5 + x Combine like terms: -1 + -5 = -6 -6 + 4x + x + 5x2 = -5 + x Combine like terms: 4x + x = 5x -6 + 5x + 5x2 = -5 + x Solving -6 + 5x + 5x2 = -5 + x Solving for variable 'x'. Reorder the terms: -6 + 5 + 5x + -1x + 5x2 = -5 + x + 5 + -1x Combine like terms: -6 + 5 = -1 -1 + 5x + -1x + 5x2 = -5 + x + 5 + -1x Combine like terms: 5x + -1x = 4x -1 + 4x + 5x2 = -5 + x + 5 + -1x Reorder the terms: -1 + 4x + 5x2 = -5 + 5 + x + -1x Combine like terms: -5 + 5 = 0 -1 + 4x + 5x2 = 0 + x + -1x -1 + 4x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -1 + 4x + 5x2 = 0 Factor a trinomial. (-1 + -1x)(1 + -5x) = 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 '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {-1, 0.2}
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