10n^2-30=3n^2-37n

Solution for 10n^2-30=3n^2-37n equation:

Simplifying
10n2 + -30 = 3n2 + -37n

Reorder the terms:
-30 + 10n2 = 3n2 + -37n

Reorder the terms:
-30 + 10n2 = -37n + 3n2

Solving
-30 + 10n2 = -37n + 3n2

Solving for variable 'n'.

Reorder the terms:
-30 + 37n + 10n2 + -3n2 = -37n + 3n2 + 37n + -3n2

Combine like terms: 10n2 + -3n2 = 7n2
-30 + 37n + 7n2 = -37n + 3n2 + 37n + -3n2

Reorder the terms:
-30 + 37n + 7n2 = -37n + 37n + 3n2 + -3n2

Combine like terms: -37n + 37n = 0
-30 + 37n + 7n2 = 0 + 3n2 + -3n2
-30 + 37n + 7n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
-30 + 37n + 7n2 = 0

Factor a trinomial.
(-6 + -1n)(5 + -7n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(5 + -7n)' equal to zero and attempt to solve:

Simplifying
5 + -7n = 0

Solving
5 + -7n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -7n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7n = 0 + -5
-7n = 0 + -5

Combine like terms: 0 + -5 = -5
-7n = -5

Divide each side by '-7'.
n = 0.7142857143

Simplifying
n = 0.7142857143
Solution
n = {-6, 0.7142857143}