2u^2=5u+3

Solution for 2u^2=5u+3 equation:

Simplifying
2u2 = 5u + 3

Reorder the terms:
2u2 = 3 + 5u

Solving
2u2 = 3 + 5u

Solving for variable 'u'.

Reorder the terms:
-3 + -5u + 2u2 = 3 + 5u + -3 + -5u

Reorder the terms:
-3 + -5u + 2u2 = 3 + -3 + 5u + -5u

Combine like terms: 3 + -3 = 0
-3 + -5u + 2u2 = 0 + 5u + -5u
-3 + -5u + 2u2 = 5u + -5u

Combine like terms: 5u + -5u = 0
-3 + -5u + 2u2 = 0

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

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

Simplifying
-1 + -2u = 0

Solving
-1 + -2u = 0

Move all terms containing u to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2u = 0 + 1
-2u = 0 + 1

Combine like terms: 0 + 1 = 1
-2u = 1

Divide each side by '-2'.
u = -0.5

Simplifying
u = -0.5
Subproblem 2
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
Solution
u = {-0.5, 3}