5(n*n-3)+3(5n*n-2)=-13n

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Solution for 5(n*n-3)+3(5n*n-2)=-13n equation: 


Simplifying
5(n * n + -3) + 3(5n * n + -2) = -13n

Multiply n * n
5(n2 + -3) + 3(5n * n + -2) = -13n

Reorder the terms:
5(-3 + n2) + 3(5n * n + -2) = -13n
(-3 * 5 + n2 * 5) + 3(5n * n + -2) = -13n
(-15 + 5n2) + 3(5n * n + -2) = -13n

Multiply n * n
-15 + 5n2 + 3(5n2 + -2) = -13n

Reorder the terms:
-15 + 5n2 + 3(-2 + 5n2) = -13n
-15 + 5n2 + (-2 * 3 + 5n2 * 3) = -13n
-15 + 5n2 + (-6 + 15n2) = -13n

Reorder the terms:
-15 + -6 + 5n2 + 15n2 = -13n

Combine like terms: -15 + -6 = -21
-21 + 5n2 + 15n2 = -13n

Combine like terms: 5n2 + 15n2 = 20n2
-21 + 20n2 = -13n

Solving
-21 + 20n2 = -13n

Solving for variable 'n'.

Reorder the terms:
-21 + 13n + 20n2 = -13n + 13n

Combine like terms: -13n + 13n = 0
-21 + 13n + 20n2 = 0

Factor a trinomial.
(-7 + -5n)(3 + -4n) = 0


Subproblem 1
Set the factor '(-7 + -5n)' equal to zero and attempt to solve:

Simplifying
-7 + -5n = 0

Solving
-7 + -5n = 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 + -5n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5n = 0 + 7
-5n = 0 + 7

Combine like terms: 0 + 7 = 7
-5n = 7

Divide each side by '-5'.
n = -1.4

Simplifying
n = -1.4

Subproblem 2
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4n = 0 + -3
-4n = 0 + -3

Combine like terms: 0 + -3 = -3
-4n = -3

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {-1.4, 0.75}

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