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Simplifying 2u2 + 6u + 13 = u2 + 10u + 25 Reorder the terms: 13 + 6u + 2u2 = u2 + 10u + 25 Reorder the terms: 13 + 6u + 2u2 = 25 + 10u + u2 Solving 13 + 6u + 2u2 = 25 + 10u + u2 Solving for variable 'u'. Reorder the terms: 13 + -25 + 6u + -10u + 2u2 + -1u2 = 25 + 10u + u2 + -25 + -10u + -1u2 Combine like terms: 13 + -25 = -12 -12 + 6u + -10u + 2u2 + -1u2 = 25 + 10u + u2 + -25 + -10u + -1u2 Combine like terms: 6u + -10u = -4u -12 + -4u + 2u2 + -1u2 = 25 + 10u + u2 + -25 + -10u + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 -12 + -4u + 1u2 = 25 + 10u + u2 + -25 + -10u + -1u2 Reorder the terms: -12 + -4u + 1u2 = 25 + -25 + 10u + -10u + u2 + -1u2 Combine like terms: 25 + -25 = 0 -12 + -4u + 1u2 = 0 + 10u + -10u + u2 + -1u2 -12 + -4u + 1u2 = 10u + -10u + u2 + -1u2 Combine like terms: 10u + -10u = 0 -12 + -4u + 1u2 = 0 + u2 + -1u2 -12 + -4u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -12 + -4u + 1u2 = 0 Factor a trinomial. (-2 + -1u)(6 + -1u) = 0Subproblem 1
Set the factor '(-2 + -1u)' equal to zero and attempt to solve: Simplifying -2 + -1u = 0 Solving -2 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1u = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1u = 0 + 2 -1u = 0 + 2 Combine like terms: 0 + 2 = 2 -1u = 2 Divide each side by '-1'. u = -2 Simplifying u = -2Subproblem 2
Set the factor '(6 + -1u)' equal to zero and attempt to solve: Simplifying 6 + -1u = 0 Solving 6 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1u = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1u = 0 + -6 -1u = 0 + -6 Combine like terms: 0 + -6 = -6 -1u = -6 Divide each side by '-1'. u = 6 Simplifying u = 6Solution
u = {-2, 6}
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