4n^2+3=7n

Solution for 4n^2+3=7n equation:

Simplifying
4n2 + 3 = 7n

Reorder the terms:
3 + 4n2 = 7n

Solving
3 + 4n2 = 7n

Solving for variable 'n'.

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

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

Factor a trinomial.
(3 + -4n)(1 + -1n) = 0

Subproblem 1
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4n = 0 + -3
-4n = 0 + -3

Combine like terms: 0 + -3 = -3
-4n = -3

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
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 = {0.75, 1}