-45n(4n+3)=15n(10n-17)

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Solution for -45n(4n+3)=15n(10n-17) equation: 


Simplifying
-45n(4n + 3) = 15n(10n + -17)

Reorder the terms:
-45n(3 + 4n) = 15n(10n + -17)
(3 * -45n + 4n * -45n) = 15n(10n + -17)
(-135n + -180n2) = 15n(10n + -17)

Reorder the terms:
-135n + -180n2 = 15n(-17 + 10n)
-135n + -180n2 = (-17 * 15n + 10n * 15n)
-135n + -180n2 = (-255n + 150n2)

Solving
-135n + -180n2 = -255n + 150n2

Solving for variable 'n'.

Reorder the terms:
-135n + 255n + -180n2 + -150n2 = -255n + 150n2 + 255n + -150n2

Combine like terms: -135n + 255n = 120n
120n + -180n2 + -150n2 = -255n + 150n2 + 255n + -150n2

Combine like terms: -180n2 + -150n2 = -330n2
120n + -330n2 = -255n + 150n2 + 255n + -150n2

Reorder the terms:
120n + -330n2 = -255n + 255n + 150n2 + -150n2

Combine like terms: -255n + 255n = 0
120n + -330n2 = 0 + 150n2 + -150n2
120n + -330n2 = 150n2 + -150n2

Combine like terms: 150n2 + -150n2 = 0
120n + -330n2 = 0

Factor out the Greatest Common Factor (GCF), '30n'.
30n(4 + -11n) = 0

Ignore the factor 30.

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(4 + -11n)' equal to zero and attempt to solve:

Simplifying
4 + -11n = 0

Solving
4 + -11n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -11n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -11n = 0 + -4
-11n = 0 + -4

Combine like terms: 0 + -4 = -4
-11n = -4

Divide each side by '-11'.
n = 0.3636363636

Simplifying
n = 0.3636363636
Solution
n = {0, 0.3636363636}

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