4n^2-8n+14=10

Solution for 4n^2-8n+14=10 equation:

Simplifying
4n2 + -8n + 14 = 10

Reorder the terms:
14 + -8n + 4n2 = 10

Solving
14 + -8n + 4n2 = 10

Solving for variable 'n'.

Reorder the terms:
14 + -10 + -8n + 4n2 = 10 + -10

Combine like terms: 14 + -10 = 4
4 + -8n + 4n2 = 10 + -10

Combine like terms: 10 + -10 = 0
4 + -8n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -2n + n2) = 0

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {1, 1}