21(n-4)+21n=10n(n-4)

Solution for 21(n-4)+21n=10n(n-4) equation:

Simplifying
21(n + -4) + 21n = 10n(n + -4)

Reorder the terms:
21(-4 + n) + 21n = 10n(n + -4)
(-4 * 21 + n * 21) + 21n = 10n(n + -4)
(-84 + 21n) + 21n = 10n(n + -4)

Combine like terms: 21n + 21n = 42n
-84 + 42n = 10n(n + -4)

Reorder the terms:
-84 + 42n = 10n(-4 + n)
-84 + 42n = (-4 * 10n + n * 10n)
-84 + 42n = (-40n + 10n2)

Solving
-84 + 42n = -40n + 10n2

Solving for variable 'n'.

Combine like terms: 42n + 40n = 82n
-84 + 82n + -10n2 = -40n + 10n2 + 40n + -10n2

Reorder the terms:
-84 + 82n + -10n2 = -40n + 40n + 10n2 + -10n2

Combine like terms: -40n + 40n = 0
-84 + 82n + -10n2 = 0 + 10n2 + -10n2
-84 + 82n + -10n2 = 10n2 + -10n2

Combine like terms: 10n2 + -10n2 = 0
-84 + 82n + -10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + 41n + -5n2) = 0

Factor a trinomial.
2((-7 + n)(6 + -5n)) = 0

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

Simplifying
-7 + n = 0

Solving
-7 + n = 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 + n = 0 + 7

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

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

Simplifying
n = 7
Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {7, 1.2}