4u^2-6=-5u

Solution for 4u^2-6=-5u equation:

Simplifying
4u2 + -6 = -5u

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

Solving
-6 + 4u2 = -5u

Solving for variable 'u'.

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

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

Factor a trinomial.
(-2 + -1u)(3 + -4u) = 0

Subproblem 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 = -2
Subproblem 2
Set the factor '(3 + -4u)' equal to zero and attempt to solve:

Simplifying
3 + -4u = 0

Solving
3 + -4u = 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 + -4u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4u = 0 + -3
-4u = 0 + -3

Combine like terms: 0 + -3 = -3
-4u = -3

Divide each side by '-4'.
u = 0.75

Simplifying
u = 0.75
Solution
u = {-2, 0.75}