(4n+22)(8n-10)=180

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Solution for (4n+22)(8n-10)=180 equation: 


Simplifying
(4n + 22)(8n + -10) = 180

Reorder the terms:
(22 + 4n)(8n + -10) = 180

Reorder the terms:
(22 + 4n)(-10 + 8n) = 180

Multiply (22 + 4n) * (-10 + 8n)
(22(-10 + 8n) + 4n * (-10 + 8n)) = 180
((-10 * 22 + 8n * 22) + 4n * (-10 + 8n)) = 180
((-220 + 176n) + 4n * (-10 + 8n)) = 180
(-220 + 176n + (-10 * 4n + 8n * 4n)) = 180
(-220 + 176n + (-40n + 32n2)) = 180

Combine like terms: 176n + -40n = 136n
(-220 + 136n + 32n2) = 180

Solving
-220 + 136n + 32n2 = 180

Solving for variable 'n'.

Reorder the terms:
-220 + -180 + 136n + 32n2 = 180 + -180

Combine like terms: -220 + -180 = -400
-400 + 136n + 32n2 = 180 + -180

Combine like terms: 180 + -180 = 0
-400 + 136n + 32n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-50 + 17n + 4n2) = 0

Factor a trinomial.
8((-25 + -4n)(2 + -1n)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-25 + -4n)' equal to zero and attempt to solve:

Simplifying
-25 + -4n = 0

Solving
-25 + -4n = 0

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

Add '25' to each side of the equation.
-25 + 25 + -4n = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -4n = 0 + 25
-4n = 0 + 25

Combine like terms: 0 + 25 = 25
-4n = 25

Divide each side by '-4'.
n = -6.25

Simplifying
n = -6.25

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 = {-6.25, 2}

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