2u^2=3u+2

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

Simplifying
2u2 = 3u + 2

Reorder the terms:
2u2 = 2 + 3u

Solving
2u2 = 2 + 3u

Solving for variable 'u'.

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

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

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

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

Factor a trinomial.
(-1 + -2u)(2 + -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 '(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 = {-0.5, 2}