2n(n+1)=7n-2

Solution for 2n(n+1)=7n-2 equation:

Simplifying
2n(n + 1) = 7n + -2

Reorder the terms:
2n(1 + n) = 7n + -2
(1 * 2n + n * 2n) = 7n + -2
(2n + 2n2) = 7n + -2

Reorder the terms:
2n + 2n2 = -2 + 7n

Solving
2n + 2n2 = -2 + 7n

Solving for variable 'n'.

Reorder the terms:
2 + 2n + -7n + 2n2 = -2 + 7n + 2 + -7n

Combine like terms: 2n + -7n = -5n
2 + -5n + 2n2 = -2 + 7n + 2 + -7n

Reorder the terms:
2 + -5n + 2n2 = -2 + 2 + 7n + -7n

Combine like terms: -2 + 2 = 0
2 + -5n + 2n2 = 0 + 7n + -7n
2 + -5n + 2n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
2 + -5n + 2n2 = 0

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

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

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

Simplifying
n = 0.5
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {0.5, 2}