9n^2+50n=35-3n(1+3n)

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Solution for 9n^2+50n=35-3n(1+3n) equation: 


Simplifying
9n2 + 50n = 35 + -3n(1 + 3n)

Reorder the terms:
50n + 9n2 = 35 + -3n(1 + 3n)
50n + 9n2 = 35 + (1 * -3n + 3n * -3n)
50n + 9n2 = 35 + (-3n + -9n2)

Solving
50n + 9n2 = 35 + -3n + -9n2

Solving for variable 'n'.

Reorder the terms:
-35 + 50n + 3n + 9n2 + 9n2 = 35 + -3n + -9n2 + -35 + 3n + 9n2

Combine like terms: 50n + 3n = 53n
-35 + 53n + 9n2 + 9n2 = 35 + -3n + -9n2 + -35 + 3n + 9n2

Combine like terms: 9n2 + 9n2 = 18n2
-35 + 53n + 18n2 = 35 + -3n + -9n2 + -35 + 3n + 9n2

Reorder the terms:
-35 + 53n + 18n2 = 35 + -35 + -3n + 3n + -9n2 + 9n2

Combine like terms: 35 + -35 = 0
-35 + 53n + 18n2 = 0 + -3n + 3n + -9n2 + 9n2
-35 + 53n + 18n2 = -3n + 3n + -9n2 + 9n2

Combine like terms: -3n + 3n = 0
-35 + 53n + 18n2 = 0 + -9n2 + 9n2
-35 + 53n + 18n2 = -9n2 + 9n2

Combine like terms: -9n2 + 9n2 = 0
-35 + 53n + 18n2 = 0

Factor a trinomial.
(-7 + -2n)(5 + -9n) = 0


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

Simplifying
-7 + -2n = 0

Solving
-7 + -2n = 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 + -2n = 0 + 7

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

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

Divide each side by '-2'.
n = -3.5

Simplifying
n = -3.5

Subproblem 2
Set the factor '(5 + -9n)' equal to zero and attempt to solve:

Simplifying
5 + -9n = 0

Solving
5 + -9n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -9n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9n = 0 + -5
-9n = 0 + -5

Combine like terms: 0 + -5 = -5
-9n = -5

Divide each side by '-9'.
n = 0.5555555556

Simplifying
n = 0.5555555556
Solution
n = {-3.5, 0.5555555556}

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