20(2n-1)=11(n-1)(n-2)

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Solution for 20(2n-1)=11(n-1)(n-2) equation: 


Simplifying
20(2n + -1) = 11(n + -1)(n + -2)

Reorder the terms:
20(-1 + 2n) = 11(n + -1)(n + -2)
(-1 * 20 + 2n * 20) = 11(n + -1)(n + -2)
(-20 + 40n) = 11(n + -1)(n + -2)

Reorder the terms:
-20 + 40n = 11(-1 + n)(n + -2)

Reorder the terms:
-20 + 40n = 11(-1 + n)(-2 + n)

Multiply (-1 + n) * (-2 + n)
-20 + 40n = 11(-1(-2 + n) + n(-2 + n))
-20 + 40n = 11((-2 * -1 + n * -1) + n(-2 + n))
-20 + 40n = 11((2 + -1n) + n(-2 + n))
-20 + 40n = 11(2 + -1n + (-2 * n + n * n))
-20 + 40n = 11(2 + -1n + (-2n + n2))

Combine like terms: -1n + -2n = -3n
-20 + 40n = 11(2 + -3n + n2)
-20 + 40n = (2 * 11 + -3n * 11 + n2 * 11)
-20 + 40n = (22 + -33n + 11n2)

Solving
-20 + 40n = 22 + -33n + 11n2

Solving for variable 'n'.

Reorder the terms:
-20 + -22 + 40n + 33n + -11n2 = 22 + -33n + 11n2 + -22 + 33n + -11n2

Combine like terms: -20 + -22 = -42
-42 + 40n + 33n + -11n2 = 22 + -33n + 11n2 + -22 + 33n + -11n2

Combine like terms: 40n + 33n = 73n
-42 + 73n + -11n2 = 22 + -33n + 11n2 + -22 + 33n + -11n2

Reorder the terms:
-42 + 73n + -11n2 = 22 + -22 + -33n + 33n + 11n2 + -11n2

Combine like terms: 22 + -22 = 0
-42 + 73n + -11n2 = 0 + -33n + 33n + 11n2 + -11n2
-42 + 73n + -11n2 = -33n + 33n + 11n2 + -11n2

Combine like terms: -33n + 33n = 0
-42 + 73n + -11n2 = 0 + 11n2 + -11n2
-42 + 73n + -11n2 = 11n2 + -11n2

Combine like terms: 11n2 + -11n2 = 0
-42 + 73n + -11n2 = 0

Factor a trinomial.
(-6 + n)(7 + -11n) = 0


Subproblem 1
Set the factor '(-6 + n)' equal to zero and attempt to solve:

Simplifying
-6 + n = 0

Solving
-6 + n = 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 + n = 0 + 6

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

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

Simplifying
n = 6

Subproblem 2
Set the factor '(7 + -11n)' equal to zero and attempt to solve:

Simplifying
7 + -11n = 0

Solving
7 + -11n = 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 + -11n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -11n = 0 + -7
-11n = 0 + -7

Combine like terms: 0 + -7 = -7
-11n = -7

Divide each side by '-11'.
n = 0.6363636364

Simplifying
n = 0.6363636364
Solution
n = {6, 0.6363636364}

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