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

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

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

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

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

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

Solving for variable 'n'.

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

Combine like terms: 20n + -3n = 17n
3 + 17n + 10n2 = -3 + 3n + 3 + -3n

Reorder the terms:
3 + 17n + 10n2 = -3 + 3 + 3n + -3n

Combine like terms: -3 + 3 = 0
3 + 17n + 10n2 = 0 + 3n + -3n
3 + 17n + 10n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
3 + 17n + 10n2 = 0

Factor a trinomial.
(3 + 2n)(1 + 5n) = 0

Subproblem 1
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

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

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

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(1 + 5n)' equal to zero and attempt to solve:

Simplifying
1 + 5n = 0

Solving
1 + 5n = 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 + 5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5n = 0 + -1
5n = 0 + -1

Combine like terms: 0 + -1 = -1
5n = -1

Divide each side by '5'.
n = -0.2

Simplifying
n = -0.2
Solution
n = {-1.5, -0.2}