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Simplifying (x + -4)(x) + (2x + -1) = x + -1(4 + -1x) Reorder the terms: (-4 + x)(x) + (2x + -1) = x + -1(4 + -1x) Reorder the terms for easier multiplication: x(-4 + x) + (2x + -1) = x + -1(4 + -1x) (-4 * x + x * x) + (2x + -1) = x + -1(4 + -1x) (-4x + x2) + (2x + -1) = x + -1(4 + -1x) Reorder the terms: -4x + x2 + (-1 + 2x) = x + -1(4 + -1x) Remove parenthesis around (-1 + 2x) -4x + x2 + -1 + 2x = x + -1(4 + -1x) Reorder the terms: -1 + -4x + 2x + x2 = x + -1(4 + -1x) Combine like terms: -4x + 2x = -2x -1 + -2x + x2 = x + -1(4 + -1x) -1 + -2x + x2 = x + (4 * -1 + -1x * -1) -1 + -2x + x2 = x + (-4 + 1x) Reorder the terms: -1 + -2x + x2 = -4 + x + 1x Combine like terms: x + 1x = 2x -1 + -2x + x2 = -4 + 2x Solving -1 + -2x + x2 = -4 + 2x Solving for variable 'x'. Reorder the terms: -1 + 4 + -2x + -2x + x2 = -4 + 2x + 4 + -2x Combine like terms: -1 + 4 = 3 3 + -2x + -2x + x2 = -4 + 2x + 4 + -2x Combine like terms: -2x + -2x = -4x 3 + -4x + x2 = -4 + 2x + 4 + -2x Reorder the terms: 3 + -4x + x2 = -4 + 4 + 2x + -2x Combine like terms: -4 + 4 = 0 3 + -4x + x2 = 0 + 2x + -2x 3 + -4x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 3 + -4x + x2 = 0 Factor a trinomial. (1 + -1x)(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {1, 3}
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