5u^2-6=7u

Solution for 5u^2-6=7u equation:

Simplifying
5u2 + -6 = 7u

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

Solving
-6 + 5u2 = 7u

Solving for variable 'u'.

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

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

Factor a trinomial.
(-3 + -5u)(2 + -1u) = 0

Subproblem 1
Set the factor '(-3 + -5u)' equal to zero and attempt to solve:

Simplifying
-3 + -5u = 0

Solving
-3 + -5u = 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 + -5u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5u = 0 + 3
-5u = 0 + 3

Combine like terms: 0 + 3 = 3
-5u = 3

Divide each side by '-5'.
u = -0.6

Simplifying
u = -0.6
Subproblem 2
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 = 2
Solution
u = {-0.6, 2}