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Simplifying 126 = (7 + -1x)(12 + -1x) Multiply (7 + -1x) * (12 + -1x) 126 = (7(12 + -1x) + -1x * (12 + -1x)) 126 = ((12 * 7 + -1x * 7) + -1x * (12 + -1x)) 126 = ((84 + -7x) + -1x * (12 + -1x)) 126 = (84 + -7x + (12 * -1x + -1x * -1x)) 126 = (84 + -7x + (-12x + 1x2)) Combine like terms: -7x + -12x = -19x 126 = (84 + -19x + 1x2) Solving 126 = 84 + -19x + 1x2 Solving for variable 'x'. Combine like terms: 126 + -84 = 42 42 + 19x + -1x2 = 84 + -19x + 1x2 + -84 + 19x + -1x2 Reorder the terms: 42 + 19x + -1x2 = 84 + -84 + -19x + 19x + 1x2 + -1x2 Combine like terms: 84 + -84 = 0 42 + 19x + -1x2 = 0 + -19x + 19x + 1x2 + -1x2 42 + 19x + -1x2 = -19x + 19x + 1x2 + -1x2 Combine like terms: -19x + 19x = 0 42 + 19x + -1x2 = 0 + 1x2 + -1x2 42 + 19x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 42 + 19x + -1x2 = 0 Factor a trinomial. (21 + -1x)(2 + x) = 0Subproblem 1
Set the factor '(21 + -1x)' equal to zero and attempt to solve: Simplifying 21 + -1x = 0 Solving 21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1x = 0 + -21 -1x = 0 + -21 Combine like terms: 0 + -21 = -21 -1x = -21 Divide each side by '-1'. x = 21 Simplifying x = 21Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {21, -2}
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