n(n-3)=70

Solution for n(n-3)=70 equation:

Simplifying
n(n + -3) = 70

Reorder the terms:
n(-3 + n) = 70
(-3 * n + n * n) = 70
(-3n + n2) = 70

Solving
-3n + n2 = 70

Solving for variable 'n'.

Reorder the terms:
-70 + -3n + n2 = 70 + -70

Combine like terms: 70 + -70 = 0
-70 + -3n + n2 = 0

Factor a trinomial.
(-7 + -1n)(10 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {-7, 10}