(u^2-6u+4)+(-7u^2+3u+5)=0

Solution for (u^2-6u+4)+(-7u^2+3u+5)=0 equation:

Simplifying
(u2 + -6u + 4) + (-7u2 + 3u + 5) = 0

Reorder the terms:
(4 + -6u + u2) + (-7u2 + 3u + 5) = 0

Remove parenthesis around (4 + -6u + u2)
4 + -6u + u2 + (-7u2 + 3u + 5) = 0

Reorder the terms:
4 + -6u + u2 + (5 + 3u + -7u2) = 0

Remove parenthesis around (5 + 3u + -7u2)
4 + -6u + u2 + 5 + 3u + -7u2 = 0

Reorder the terms:
4 + 5 + -6u + 3u + u2 + -7u2 = 0

Combine like terms: 4 + 5 = 9
9 + -6u + 3u + u2 + -7u2 = 0

Combine like terms: -6u + 3u = -3u
9 + -3u + u2 + -7u2 = 0

Combine like terms: u2 + -7u2 = -6u2
9 + -3u + -6u2 = 0

Solving
9 + -3u + -6u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -1u + -2u2) = 0

Factor a trinomial.
3((1 + -1u)(3 + 2u)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -1u)' equal to zero and attempt to solve:

Simplifying
1 + -1u = 0

Solving
1 + -1u = 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 + -1u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1u = 0 + -1
-1u = 0 + -1

Combine like terms: 0 + -1 = -1
-1u = -1

Divide each side by '-1'.
u = 1

Simplifying
u = 1
Subproblem 2
Set the factor '(3 + 2u)' equal to zero and attempt to solve:

Simplifying
3 + 2u = 0

Solving
3 + 2u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2u = 0 + -3
2u = 0 + -3

Combine like terms: 0 + -3 = -3
2u = -3

Divide each side by '2'.
u = -1.5

Simplifying
u = -1.5
Solution
u = {1, -1.5}