4n(2n-5)=3n+10

Solution for 4n(2n-5)=3n+10 equation:

Simplifying
4n(2n + -5) = 3n + 10

Reorder the terms:
4n(-5 + 2n) = 3n + 10
(-5 * 4n + 2n * 4n) = 3n + 10
(-20n + 8n2) = 3n + 10

Reorder the terms:
-20n + 8n2 = 10 + 3n

Solving
-20n + 8n2 = 10 + 3n

Solving for variable 'n'.

Reorder the terms:
-10 + -20n + -3n + 8n2 = 10 + 3n + -10 + -3n

Combine like terms: -20n + -3n = -23n
-10 + -23n + 8n2 = 10 + 3n + -10 + -3n

Reorder the terms:
-10 + -23n + 8n2 = 10 + -10 + 3n + -3n

Combine like terms: 10 + -10 = 0
-10 + -23n + 8n2 = 0 + 3n + -3n
-10 + -23n + 8n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-10 + -23n + 8n2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-1.25 + -2.875n + n2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -2.875n + 1.25 + n2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -2.875n + n2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -2.875n + n2 = 0 + 1.25
-2.875n + n2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-2.875n + n2 = 1.25

The n term is -2.875n.  Take half its coefficient (-1.4375).
Square it (2.06640625) and add it to both sides.

Add '2.06640625' to each side of the equation.
-2.875n + 2.06640625 + n2 = 1.25 + 2.06640625

Reorder the terms:
2.06640625 + -2.875n + n2 = 1.25 + 2.06640625

Combine like terms: 1.25 + 2.06640625 = 3.31640625
2.06640625 + -2.875n + n2 = 3.31640625

Factor a perfect square on the left side:
(n + -1.4375)(n + -1.4375) = 3.31640625

Calculate the square root of the right side: 1.821100286

Break this problem into two subproblems by setting 
(n + -1.4375) equal to 1.821100286 and -1.821100286.

Subproblem 1
n + -1.4375 = 1.821100286

Simplifying
n + -1.4375 = 1.821100286

Reorder the terms:
-1.4375 + n = 1.821100286

Solving
-1.4375 + n = 1.821100286

Solving for variable 'n'.

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

Add '1.4375' to each side of the equation.
-1.4375 + 1.4375 + n = 1.821100286 + 1.4375

Combine like terms: -1.4375 + 1.4375 = 0.0000
0.0000 + n = 1.821100286 + 1.4375
n = 1.821100286 + 1.4375

Combine like terms: 1.821100286 + 1.4375 = 3.258600286
n = 3.258600286

Simplifying
n = 3.258600286

Subproblem 2
n + -1.4375 = -1.821100286

Simplifying
n + -1.4375 = -1.821100286

Reorder the terms:
-1.4375 + n = -1.821100286

Solving
-1.4375 + n = -1.821100286

Solving for variable 'n'.

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

Add '1.4375' to each side of the equation.
-1.4375 + 1.4375 + n = -1.821100286 + 1.4375

Combine like terms: -1.4375 + 1.4375 = 0.0000
0.0000 + n = -1.821100286 + 1.4375
n = -1.821100286 + 1.4375

Combine like terms: -1.821100286 + 1.4375 = -0.383600286
n = -0.383600286

Simplifying
n = -0.383600286

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.258600286, -0.383600286}