5n^2+3n=4-2n^2

Solution for 5n^2+3n=4-2n^2 equation:

Simplifying
5n2 + 3n = 4 + -2n2

Reorder the terms:
3n + 5n2 = 4 + -2n2

Solving
3n + 5n2 = 4 + -2n2

Solving for variable 'n'.

Reorder the terms:
-4 + 3n + 5n2 + 2n2 = 4 + -2n2 + -4 + 2n2

Combine like terms: 5n2 + 2n2 = 7n2
-4 + 3n + 7n2 = 4 + -2n2 + -4 + 2n2

Reorder the terms:
-4 + 3n + 7n2 = 4 + -4 + -2n2 + 2n2

Combine like terms: 4 + -4 = 0
-4 + 3n + 7n2 = 0 + -2n2 + 2n2
-4 + 3n + 7n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
-4 + 3n + 7n2 = 0

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

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

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

Simplifying
n = -1
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 = {-1, 0.5714285714}