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Simplifying 240 = (x + -6)(x + -14) Reorder the terms: 240 = (-6 + x)(x + -14) Reorder the terms: 240 = (-6 + x)(-14 + x) Multiply (-6 + x) * (-14 + x) 240 = (-6(-14 + x) + x(-14 + x)) 240 = ((-14 * -6 + x * -6) + x(-14 + x)) 240 = ((84 + -6x) + x(-14 + x)) 240 = (84 + -6x + (-14 * x + x * x)) 240 = (84 + -6x + (-14x + x2)) Combine like terms: -6x + -14x = -20x 240 = (84 + -20x + x2) Solving 240 = 84 + -20x + x2 Solving for variable 'x'. Combine like terms: 240 + -84 = 156 156 + 20x + -1x2 = 84 + -20x + x2 + -84 + 20x + -1x2 Reorder the terms: 156 + 20x + -1x2 = 84 + -84 + -20x + 20x + x2 + -1x2 Combine like terms: 84 + -84 = 0 156 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2 156 + 20x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 156 + 20x + -1x2 = 0 + x2 + -1x2 156 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 156 + 20x + -1x2 = 0 Factor a trinomial. (26 + -1x)(6 + x) = 0Subproblem 1
Set the factor '(26 + -1x)' equal to zero and attempt to solve: Simplifying 26 + -1x = 0 Solving 26 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + -1x = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -1x = 0 + -26 -1x = 0 + -26 Combine like terms: 0 + -26 = -26 -1x = -26 Divide each side by '-1'. x = 26 Simplifying x = 26Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {26, -6}
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