(n+4r)n^2-(7n+r)n^2=

Solution for (n+4r)n^2-(7n+r)n^2= equation:

Simplifying
(n + 4r) * n2 + -1(7n + r) * n2 = 0

Reorder the terms for easier multiplication:
n2(n + 4r) + -1(7n + r) * n2 = 0
(n * n2 + 4r * n2) + -1(7n + r) * n2 = 0

Reorder the terms:
(4n2r + n3) + -1(7n + r) * n2 = 0
(4n2r + n3) + -1(7n + r) * n2 = 0

Reorder the terms for easier multiplication:
4n2r + n3 + -1n2(7n + r) = 0
4n2r + n3 + (7n * -1n2 + r * -1n2) = 0

Reorder the terms:
4n2r + n3 + (-1n2r + -7n3) = 0
4n2r + n3 + (-1n2r + -7n3) = 0

Reorder the terms:
4n2r + -1n2r + n3 + -7n3 = 0

Combine like terms: 4n2r + -1n2r = 3n2r
3n2r + n3 + -7n3 = 0

Combine like terms: n3 + -7n3 = -6n3
3n2r + -6n3 = 0

Solving
3n2r + -6n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n2'.
3n2(r + -2n) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(r + -2n)' equal to zero and attempt to solve:

Simplifying
r + -2n = 0

Reorder the terms:
-2n + r = 0

Solving
-2n + r = 0

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

Add '-1r' to each side of the equation.
-2n + r + -1r = 0 + -1r

Combine like terms: r + -1r = 0
-2n + 0 = 0 + -1r
-2n = 0 + -1r
Remove the zero:
-2n = -1r

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

Simplifying
n = 0.5r
Solution
n = {0, 0.5r}