3n^2+10n=2n^2-42

Solution for 3n^2+10n=2n^2-42 equation:

Simplifying
3n2 + 10n = 2n2 + -42

Reorder the terms:
10n + 3n2 = 2n2 + -42

Reorder the terms:
10n + 3n2 = -42 + 2n2

Solving
10n + 3n2 = -42 + 2n2

Solving for variable 'n'.

Reorder the terms:
42 + 10n + 3n2 + -2n2 = -42 + 2n2 + 42 + -2n2

Combine like terms: 3n2 + -2n2 = 1n2
42 + 10n + 1n2 = -42 + 2n2 + 42 + -2n2

Reorder the terms:
42 + 10n + 1n2 = -42 + 42 + 2n2 + -2n2

Combine like terms: -42 + 42 = 0
42 + 10n + 1n2 = 0 + 2n2 + -2n2
42 + 10n + 1n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
42 + 10n + 1n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + 10n + -42 + n2 = 0 + -42

Reorder the terms:
42 + -42 + 10n + n2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 10n + n2 = 0 + -42
10n + n2 = 0 + -42

Combine like terms: 0 + -42 = -42
10n + n2 = -42

The n term is 10n.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10n + 25 + n2 = -42 + 25

Reorder the terms:
25 + 10n + n2 = -42 + 25

Combine like terms: -42 + 25 = -17
25 + 10n + n2 = -17

Factor a perfect square on the left side:
(n + 5)(n + 5) = -17

Can't calculate square root of the right side.

The solution to this equation could not be determined.