1-4n=-5n^2+2

Solution for 1-4n=-5n^2+2 equation:

Simplifying
1 + -4n = -5n2 + 2

Reorder the terms:
1 + -4n = 2 + -5n2

Solving
1 + -4n = 2 + -5n2

Solving for variable 'n'.

Reorder the terms:
1 + -2 + -4n + 5n2 = 2 + -5n2 + -2 + 5n2

Combine like terms: 1 + -2 = -1
-1 + -4n + 5n2 = 2 + -5n2 + -2 + 5n2

Reorder the terms:
-1 + -4n + 5n2 = 2 + -2 + -5n2 + 5n2

Combine like terms: 2 + -2 = 0
-1 + -4n + 5n2 = 0 + -5n2 + 5n2
-1 + -4n + 5n2 = -5n2 + 5n2

Combine like terms: -5n2 + 5n2 = 0
-1 + -4n + 5n2 = 0

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

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

Simplifying
-1 + -5n = 0

Solving
-1 + -5n = 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 + -5n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5n = 0 + 1
-5n = 0 + 1

Combine like terms: 0 + 1 = 1
-5n = 1

Divide each side by '-5'.
n = -0.2

Simplifying
n = -0.2
Subproblem 2
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
Solution
n = {-0.2, 1}