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Simplifying 2x(x + 1) = 4 + -5x Reorder the terms: 2x(1 + x) = 4 + -5x (1 * 2x + x * 2x) = 4 + -5x (2x + 2x2) = 4 + -5x Solving 2x + 2x2 = 4 + -5x Solving for variable 'x'. Reorder the terms: -4 + 2x + 5x + 2x2 = 4 + -5x + -4 + 5x Combine like terms: 2x + 5x = 7x -4 + 7x + 2x2 = 4 + -5x + -4 + 5x Reorder the terms: -4 + 7x + 2x2 = 4 + -4 + -5x + 5x Combine like terms: 4 + -4 = 0 -4 + 7x + 2x2 = 0 + -5x + 5x -4 + 7x + 2x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -4 + 7x + 2x2 = 0 Factor a trinomial. (-4 + -1x)(1 + -2x) = 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 '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-4, 0.5}
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