-5u=4u^2-6

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

Simplifying
-5u = 4u2 + -6

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

Solving
-5u = -6 + 4u2

Solving for variable 'u'.

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

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

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

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

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

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

Simplifying
2 + u = 0

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

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

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

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