-3n(2n-5)=0.5(-12n+30)

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Solution for -3n(2n-5)=0.5(-12n+30) equation: 


Simplifying
-3n(2n + -5) = 0.5(-12n + 30)

Reorder the terms:
-3n(-5 + 2n) = 0.5(-12n + 30)
(-5 * -3n + 2n * -3n) = 0.5(-12n + 30)
(15n + -6n2) = 0.5(-12n + 30)

Reorder the terms:
15n + -6n2 = 0.5(30 + -12n)
15n + -6n2 = (30 * 0.5 + -12n * 0.5)
15n + -6n2 = (15 + -6n)

Solving
15n + -6n2 = 15 + -6n

Solving for variable 'n'.

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

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

Reorder the terms:
-15 + 21n + -6n2 = 15 + -15 + -6n + 6n

Combine like terms: 15 + -15 = 0
-15 + 21n + -6n2 = 0 + -6n + 6n
-15 + 21n + -6n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
-15 + 21n + -6n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 7n + -2n2) = 0

Factor a trinomial.
3((-5 + 2n)(1 + -1n)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + 2n)' equal to zero and attempt to solve:

Simplifying
-5 + 2n = 0

Solving
-5 + 2n = 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 + 2n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2n = 0 + 5
2n = 0 + 5

Combine like terms: 0 + 5 = 5
2n = 5

Divide each side by '2'.
n = 2.5

Simplifying
n = 2.5

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {2.5, 1}

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