4n^2-7=27n

Solution for 4n^2-7=27n equation:

Simplifying
4n2 + -7 = 27n

Reorder the terms:
-7 + 4n2 = 27n

Solving
-7 + 4n2 = 27n

Solving for variable 'n'.

Reorder the terms:
-7 + -27n + 4n2 = 27n + -27n

Combine like terms: 27n + -27n = 0
-7 + -27n + 4n2 = 0

Factor a trinomial.
(-1 + -4n)(7 + -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 '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-0.25, 7}