7n^2+52n-32=0

Solution for 7n^2+52n-32=0 equation:

Simplifying
7n2 + 52n + -32 = 0

Reorder the terms:
-32 + 52n + 7n2 = 0

Solving
-32 + 52n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-8 + -1n)(4 + -7n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(4 + -7n)' equal to zero and attempt to solve:

Simplifying
4 + -7n = 0

Solving
4 + -7n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7n = 0 + -4

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

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

Divide each side by '-7'.
n = 0.5714285714

Simplifying
n = 0.5714285714
Solution
n = {-8, 0.5714285714}