4n^2+35n+43=-4n-5n^2+3

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Solution for 4n^2+35n+43=-4n-5n^2+3 equation: 


Simplifying
4n2 + 35n + 43 = -4n + -5n2 + 3

Reorder the terms:
43 + 35n + 4n2 = -4n + -5n2 + 3

Reorder the terms:
43 + 35n + 4n2 = 3 + -4n + -5n2

Solving
43 + 35n + 4n2 = 3 + -4n + -5n2

Solving for variable 'n'.

Reorder the terms:
43 + -3 + 35n + 4n + 4n2 + 5n2 = 3 + -4n + -5n2 + -3 + 4n + 5n2

Combine like terms: 43 + -3 = 40
40 + 35n + 4n + 4n2 + 5n2 = 3 + -4n + -5n2 + -3 + 4n + 5n2

Combine like terms: 35n + 4n = 39n
40 + 39n + 4n2 + 5n2 = 3 + -4n + -5n2 + -3 + 4n + 5n2

Combine like terms: 4n2 + 5n2 = 9n2
40 + 39n + 9n2 = 3 + -4n + -5n2 + -3 + 4n + 5n2

Reorder the terms:
40 + 39n + 9n2 = 3 + -3 + -4n + 4n + -5n2 + 5n2

Combine like terms: 3 + -3 = 0
40 + 39n + 9n2 = 0 + -4n + 4n + -5n2 + 5n2
40 + 39n + 9n2 = -4n + 4n + -5n2 + 5n2

Combine like terms: -4n + 4n = 0
40 + 39n + 9n2 = 0 + -5n2 + 5n2
40 + 39n + 9n2 = -5n2 + 5n2

Combine like terms: -5n2 + 5n2 = 0
40 + 39n + 9n2 = 0

Factor a trinomial.
(8 + 3n)(5 + 3n) = 0


Subproblem 1
Set the factor '(8 + 3n)' equal to zero and attempt to solve:

Simplifying
8 + 3n = 0

Solving
8 + 3n = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3n = 0 + -8
3n = 0 + -8

Combine like terms: 0 + -8 = -8
3n = -8

Divide each side by '3'.
n = -2.666666667

Simplifying
n = -2.666666667

Subproblem 2
Set the factor '(5 + 3n)' equal to zero and attempt to solve:

Simplifying
5 + 3n = 0

Solving
5 + 3n = 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 + 3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3n = 0 + -5
3n = 0 + -5

Combine like terms: 0 + -5 = -5
3n = -5

Divide each side by '3'.
n = -1.666666667

Simplifying
n = -1.666666667
Solution
n = {-2.666666667, -1.666666667}

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