4n^2+9n+2=(4n+1)

Solution for 4n^2+9n+2=(4n+1) equation:

Simplifying
4n2 + 9n + 2 = (4n + 1)

Reorder the terms:
2 + 9n + 4n2 = (4n + 1)

Reorder the terms:
2 + 9n + 4n2 = (1 + 4n)

Remove parenthesis around (1 + 4n)
2 + 9n + 4n2 = 1 + 4n

Solving
2 + 9n + 4n2 = 1 + 4n

Solving for variable 'n'.

Reorder the terms:
2 + -1 + 9n + -4n + 4n2 = 1 + 4n + -1 + -4n

Combine like terms: 2 + -1 = 1
1 + 9n + -4n + 4n2 = 1 + 4n + -1 + -4n

Combine like terms: 9n + -4n = 5n
1 + 5n + 4n2 = 1 + 4n + -1 + -4n

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

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

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

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

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

Simplifying
1 + n = 0

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

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

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

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

Simplifying
1 + 4n = 0

Solving
1 + 4n = 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 + 4n = 0 + -1

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

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

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {-1, -0.25}