4n^2+28n-30=0

Solution for 4n^2+28n-30=0 equation:

Simplifying
4n2 + 28n + -30 = 0

Reorder the terms:
-30 + 28n + 4n2 = 0

Solving
-30 + 28n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 14n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + 14n + 2n2)' equal to zero and attempt to solve:

Simplifying
-15 + 14n + 2n2 = 0

Solving
-15 + 14n + 2n2 = 0

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

Divide each side by '2'.
-7.5 + 7n + n2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 7n + 7.5 + n2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 7n + n2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 7n + n2 = 0 + 7.5
7n + n2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
7n + n2 = 7.5

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = 7.5 + 12.25

Reorder the terms:
12.25 + 7n + n2 = 7.5 + 12.25

Combine like terms: 7.5 + 12.25 = 19.75
12.25 + 7n + n2 = 19.75

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 19.75

Calculate the square root of the right side: 4.444097209

Break this problem into two subproblems by setting 
(n + 3.5) equal to 4.444097209 and -4.444097209.

Subproblem 1
n + 3.5 = 4.444097209

Simplifying
n + 3.5 = 4.444097209

Reorder the terms:
3.5 + n = 4.444097209

Solving
3.5 + n = 4.444097209

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = 4.444097209 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = 4.444097209 + -3.5
n = 4.444097209 + -3.5

Combine like terms: 4.444097209 + -3.5 = 0.944097209
n = 0.944097209

Simplifying
n = 0.944097209

Subproblem 2
n + 3.5 = -4.444097209

Simplifying
n + 3.5 = -4.444097209

Reorder the terms:
3.5 + n = -4.444097209

Solving
3.5 + n = -4.444097209

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = -4.444097209 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = -4.444097209 + -3.5
n = -4.444097209 + -3.5

Combine like terms: -4.444097209 + -3.5 = -7.944097209
n = -7.944097209

Simplifying
n = -7.944097209

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.944097209, -7.944097209}
Solution
n = {0.944097209, -7.944097209}