2n^2=7n+4

Solution for 2n^2=7n+4 equation:

Simplifying
2n2 = 7n + 4

Reorder the terms:
2n2 = 4 + 7n

Solving
2n2 = 4 + 7n

Solving for variable 'n'.

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

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

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

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

Factor a trinomial.
(-1 + -2n)(4 + -1n) = 0

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

Simplifying
-1 + -2n = 0

Solving
-1 + -2n = 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 + -2n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2n = 0 + 1
-2n = 0 + 1

Combine like terms: 0 + 1 = 1
-2n = 1

Divide each side by '-2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

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

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

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

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-0.5, 4}