n(1+10n)-n(4n-3)=

Solution for n(1+10n)-n(4n-3)= equation:

Simplifying
n(1 + 10n) + -1n(4n + -3) = 0
(1 * n + 10n * n) + -1n(4n + -3) = 0
(1n + 10n2) + -1n(4n + -3) = 0

Reorder the terms:
1n + 10n2 + -1n(-3 + 4n) = 0
1n + 10n2 + (-3 * -1n + 4n * -1n) = 0
1n + 10n2 + (3n + -4n2) = 0

Reorder the terms:
1n + 3n + 10n2 + -4n2 = 0

Combine like terms: 1n + 3n = 4n
4n + 10n2 + -4n2 = 0

Combine like terms: 10n2 + -4n2 = 6n2
4n + 6n2 = 0

Solving
4n + 6n2 = 0

Solving for variable 'n'.

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

Ignore the factor 2.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(2 + 3n)' equal to zero and attempt to solve:

Simplifying
2 + 3n = 0

Solving
2 + 3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3n = 0 + -2
3n = 0 + -2

Combine like terms: 0 + -2 = -2
3n = -2

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Solution
n = {0, -0.6666666667}