175n^2-42n=-2n+80

Solution for 175n^2-42n=-2n+80 equation:

Simplifying
175n2 + -42n = -2n + 80

Reorder the terms:
-42n + 175n2 = -2n + 80

Reorder the terms:
-42n + 175n2 = 80 + -2n

Solving
-42n + 175n2 = 80 + -2n

Solving for variable 'n'.

Reorder the terms:
-80 + -42n + 2n + 175n2 = 80 + -2n + -80 + 2n

Combine like terms: -42n + 2n = -40n
-80 + -40n + 175n2 = 80 + -2n + -80 + 2n

Reorder the terms:
-80 + -40n + 175n2 = 80 + -80 + -2n + 2n

Combine like terms: 80 + -80 = 0
-80 + -40n + 175n2 = 0 + -2n + 2n
-80 + -40n + 175n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-80 + -40n + 175n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-16 + -8n + 35n2) = 0

Factor a trinomial.
5((-4 + -7n)(4 + -5n)) = 0

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -5n)' equal to zero and attempt to solve:

Simplifying
4 + -5n = 0

Solving
4 + -5n = 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 + -5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5n = 0 + -4
-5n = 0 + -4

Combine like terms: 0 + -4 = -4
-5n = -4

Divide each side by '-5'.
n = 0.8

Simplifying
n = 0.8
Solution
n = {-0.5714285714, 0.8}