5u^2-6=-13u

Solution for 5u^2-6=-13u equation:

Simplifying
5u2 + -6 = -13u

Reorder the terms:
-6 + 5u2 = -13u

Solving
-6 + 5u2 = -13u

Solving for variable 'u'.

Reorder the terms:
-6 + 13u + 5u2 = -13u + 13u

Combine like terms: -13u + 13u = 0
-6 + 13u + 5u2 = 0

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

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

Simplifying
-3 + -1u = 0

Solving
-3 + -1u = 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 + -1u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1u = 0 + 3
-1u = 0 + 3

Combine like terms: 0 + 3 = 3
-1u = 3

Divide each side by '-1'.
u = -3

Simplifying
u = -3
Subproblem 2
Set the factor '(2 + -5u)' equal to zero and attempt to solve:

Simplifying
2 + -5u = 0

Solving
2 + -5u = 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 + -5u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5u = 0 + -2
-5u = 0 + -2

Combine like terms: 0 + -2 = -2
-5u = -2

Divide each side by '-5'.
u = 0.4

Simplifying
u = 0.4
Solution
u = {-3, 0.4}