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Simplifying 0 = (3x2 + 2x + -5) + -1(2x2 + -1x + 5) Reorder the terms: 0 = (-5 + 2x + 3x2) + -1(2x2 + -1x + 5) Remove parenthesis around (-5 + 2x + 3x2) 0 = -5 + 2x + 3x2 + -1(2x2 + -1x + 5) Reorder the terms: 0 = -5 + 2x + 3x2 + -1(5 + -1x + 2x2) 0 = -5 + 2x + 3x2 + (5 * -1 + -1x * -1 + 2x2 * -1) 0 = -5 + 2x + 3x2 + (-5 + 1x + -2x2) Reorder the terms: 0 = -5 + -5 + 2x + 1x + 3x2 + -2x2 Combine like terms: -5 + -5 = -10 0 = -10 + 2x + 1x + 3x2 + -2x2 Combine like terms: 2x + 1x = 3x 0 = -10 + 3x + 3x2 + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 0 = -10 + 3x + 1x2 Solving 0 = -10 + 3x + 1x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -3x + -1x2 = -10 + 3x + 1x2 + 10 + -3x + -1x2 Reorder the terms: 10 + -3x + -1x2 = -10 + 10 + 3x + -3x + 1x2 + -1x2 Combine like terms: -10 + 10 = 0 10 + -3x + -1x2 = 0 + 3x + -3x + 1x2 + -1x2 10 + -3x + -1x2 = 3x + -3x + 1x2 + -1x2 Combine like terms: 3x + -3x = 0 10 + -3x + -1x2 = 0 + 1x2 + -1x2 10 + -3x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 10 + -3x + -1x2 = 0 Factor a trinomial. (2 + -1x)(5 + x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {2, -5}
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