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Simplifying 21(x + -6) + (x + -5)(6 + -1x) = 0 Reorder the terms: 21(-6 + x) + (x + -5)(6 + -1x) = 0 (-6 * 21 + x * 21) + (x + -5)(6 + -1x) = 0 (-126 + 21x) + (x + -5)(6 + -1x) = 0 Reorder the terms: -126 + 21x + (-5 + x)(6 + -1x) = 0 Multiply (-5 + x) * (6 + -1x) -126 + 21x + (-5(6 + -1x) + x(6 + -1x)) = 0 -126 + 21x + ((6 * -5 + -1x * -5) + x(6 + -1x)) = 0 -126 + 21x + ((-30 + 5x) + x(6 + -1x)) = 0 -126 + 21x + (-30 + 5x + (6 * x + -1x * x)) = 0 -126 + 21x + (-30 + 5x + (6x + -1x2)) = 0 Combine like terms: 5x + 6x = 11x -126 + 21x + (-30 + 11x + -1x2) = 0 Reorder the terms: -126 + -30 + 21x + 11x + -1x2 = 0 Combine like terms: -126 + -30 = -156 -156 + 21x + 11x + -1x2 = 0 Combine like terms: 21x + 11x = 32x -156 + 32x + -1x2 = 0 Solving -156 + 32x + -1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-26 + x)(6 + -1x) = 0Subproblem 1
Set the factor '(-26 + x)' equal to zero and attempt to solve: Simplifying -26 + x = 0 Solving -26 + x = 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 + x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + x = 0 + 26 x = 0 + 26 Combine like terms: 0 + 26 = 26 x = 26 Simplifying x = 26Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {26, 6}
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