14n^2-18n=140+3n

Solution for 14n^2-18n=140+3n equation:

Simplifying
14n2 + -18n = 140 + 3n

Reorder the terms:
-18n + 14n2 = 140 + 3n

Solving
-18n + 14n2 = 140 + 3n

Solving for variable 'n'.

Reorder the terms:
-140 + -18n + -3n + 14n2 = 140 + 3n + -140 + -3n

Combine like terms: -18n + -3n = -21n
-140 + -21n + 14n2 = 140 + 3n + -140 + -3n

Reorder the terms:
-140 + -21n + 14n2 = 140 + -140 + 3n + -3n

Combine like terms: 140 + -140 = 0
-140 + -21n + 14n2 = 0 + 3n + -3n
-140 + -21n + 14n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-140 + -21n + 14n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-20 + -3n + 2n2) = 0

Factor a trinomial.
7((-5 + -2n)(4 + -1n)) = 0

Ignore the factor 7.
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 '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-2.5, 4}