2n^2=7n-6

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

Simplifying
2n2 = 7n + -6

Reorder the terms:
2n2 = -6 + 7n

Solving
2n2 = -6 + 7n

Solving for variable 'n'.

Reorder the terms:
6 + -7n + 2n2 = -6 + 7n + 6 + -7n

Reorder the terms:
6 + -7n + 2n2 = -6 + 6 + 7n + -7n

Combine like terms: -6 + 6 = 0
6 + -7n + 2n2 = 0 + 7n + -7n
6 + -7n + 2n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
6 + -7n + 2n2 = 0

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

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

Simplifying
3 + -2n = 0

Solving
3 + -2n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2n = 0 + -3

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

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

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

Simplifying
n = 1.5
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {1.5, 2}