4n^2-7n=2

Solution for 4n^2-7n=2 equation:

Simplifying
4n2 + -7n = 2

Reorder the terms:
-7n + 4n2 = 2

Solving
-7n + 4n2 = 2

Solving for variable 'n'.

Reorder the terms:
-2 + -7n + 4n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -7n + 4n2 = 0

Factor a trinomial.
(-1 + -4n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-1 + -4n)' equal to zero and attempt to solve:

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4n = 0 + 1
-4n = 0 + 1

Combine like terms: 0 + 1 = 1
-4n = 1

Divide each side by '-4'.
n = -0.25

Simplifying
n = -0.25
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 = {-0.25, 2}