4u^2=5u+6

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

Simplifying
4u2 = 5u + 6

Reorder the terms:
4u2 = 6 + 5u

Solving
4u2 = 6 + 5u

Solving for variable 'u'.

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

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

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

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

Factor a trinomial.
(-3 + -4u)(2 + -1u) = 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 + -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 = {-0.75, 2}