4n^2+10n-4=

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

Simplifying
4n2 + 10n + -4 = 0

Reorder the terms:
-4 + 10n + 4n2 = 0

Solving
-4 + 10n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + 5n + 2n2)' equal to zero and attempt to solve:

Simplifying
-2 + 5n + 2n2 = 0

Solving
-2 + 5n + 2n2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-1 + 2.5n + n2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.5n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.5n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.5n + n2 = 0 + 1
2.5n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.5n + n2 = 1

The n term is 2.5n.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5n + 1.5625 + n2 = 1 + 1.5625

Reorder the terms:
1.5625 + 2.5n + n2 = 1 + 1.5625

Combine like terms: 1 + 1.5625 = 2.5625
1.5625 + 2.5n + n2 = 2.5625

Factor a perfect square on the left side:
(n + 1.25)(n + 1.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(n + 1.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
n + 1.25 = 1.600781059

Simplifying
n + 1.25 = 1.600781059

Reorder the terms:
1.25 + n = 1.600781059

Solving
1.25 + n = 1.600781059

Solving for variable 'n'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + n = 1.600781059 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + n = 1.600781059 + -1.25
n = 1.600781059 + -1.25

Combine like terms: 1.600781059 + -1.25 = 0.350781059
n = 0.350781059

Simplifying
n = 0.350781059

Subproblem 2
n + 1.25 = -1.600781059

Simplifying
n + 1.25 = -1.600781059

Reorder the terms:
1.25 + n = -1.600781059

Solving
1.25 + n = -1.600781059

Solving for variable 'n'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + n = -1.600781059 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + n = -1.600781059 + -1.25
n = -1.600781059 + -1.25

Combine like terms: -1.600781059 + -1.25 = -2.850781059
n = -2.850781059

Simplifying
n = -2.850781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.350781059, -2.850781059}
Solution
n = {0.350781059, -2.850781059}