(6u^2+8u+9)-(7u^2-9u-9)+(4u^2+9u+5)=

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Solution for (6u^2+8u+9)-(7u^2-9u-9)+(4u^2+9u+5)= equation:


Simplifying
(6u2 + 8u + 9) + -1(7u2 + -9u + -9) + (4u2 + 9u + 5) = 0

Reorder the terms:
(9 + 8u + 6u2) + -1(7u2 + -9u + -9) + (4u2 + 9u + 5) = 0

Remove parenthesis around (9 + 8u + 6u2)
9 + 8u + 6u2 + -1(7u2 + -9u + -9) + (4u2 + 9u + 5) = 0

Reorder the terms:
9 + 8u + 6u2 + -1(-9 + -9u + 7u2) + (4u2 + 9u + 5) = 0
9 + 8u + 6u2 + (-9 * -1 + -9u * -1 + 7u2 * -1) + (4u2 + 9u + 5) = 0
9 + 8u + 6u2 + (9 + 9u + -7u2) + (4u2 + 9u + 5) = 0

Reorder the terms:
9 + 8u + 6u2 + 9 + 9u + -7u2 + (5 + 9u + 4u2) = 0

Remove parenthesis around (5 + 9u + 4u2)
9 + 8u + 6u2 + 9 + 9u + -7u2 + 5 + 9u + 4u2 = 0

Reorder the terms:
9 + 9 + 5 + 8u + 9u + 9u + 6u2 + -7u2 + 4u2 = 0

Combine like terms: 9 + 9 = 18
18 + 5 + 8u + 9u + 9u + 6u2 + -7u2 + 4u2 = 0

Combine like terms: 18 + 5 = 23
23 + 8u + 9u + 9u + 6u2 + -7u2 + 4u2 = 0

Combine like terms: 8u + 9u = 17u
23 + 17u + 9u + 6u2 + -7u2 + 4u2 = 0

Combine like terms: 17u + 9u = 26u
23 + 26u + 6u2 + -7u2 + 4u2 = 0

Combine like terms: 6u2 + -7u2 = -1u2
23 + 26u + -1u2 + 4u2 = 0

Combine like terms: -1u2 + 4u2 = 3u2
23 + 26u + 3u2 = 0

Solving
23 + 26u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(23 + 3u)(1 + u) = 0

Subproblem 1

Set the factor '(23 + 3u)' equal to zero and attempt to solve: Simplifying 23 + 3u = 0 Solving 23 + 3u = 0 Move all terms containing u to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 3u = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 3u = 0 + -23 3u = 0 + -23 Combine like terms: 0 + -23 = -23 3u = -23 Divide each side by '3'. u = -7.666666667 Simplifying u = -7.666666667

Subproblem 2

Set the factor '(1 + u)' equal to zero and attempt to solve: Simplifying 1 + u = 0 Solving 1 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + u = 0 + -1 u = 0 + -1 Combine like terms: 0 + -1 = -1 u = -1 Simplifying u = -1

Solution

u = {-7.666666667, -1}

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