2u^2=7u-6

Solution for 2u^2=7u-6 equation:

Simplifying
2u2 = 7u + -6

Reorder the terms:
2u2 = -6 + 7u

Solving
2u2 = -6 + 7u

Solving for variable 'u'.

Reorder the terms:
6 + -7u + 2u2 = -6 + 7u + 6 + -7u

Reorder the terms:
6 + -7u + 2u2 = -6 + 6 + 7u + -7u

Combine like terms: -6 + 6 = 0
6 + -7u + 2u2 = 0 + 7u + -7u
6 + -7u + 2u2 = 7u + -7u

Combine like terms: 7u + -7u = 0
6 + -7u + 2u2 = 0

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

Subproblem 1
Set the factor '(3 + -2u)' equal to zero and attempt to solve:

Simplifying
3 + -2u = 0

Solving
3 + -2u = 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 + -2u = 0 + -3

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

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

Divide each side by '-2'.
u = 1.5

Simplifying
u = 1.5
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 = {1.5, 2}