(4n+3)(3n-2)+5n=30

Solution for (4n+3)(3n-2)+5n=30 equation:

Simplifying
(4n + 3)(3n + -2) + 5n = 30

Reorder the terms:
(3 + 4n)(3n + -2) + 5n = 30

Reorder the terms:
(3 + 4n)(-2 + 3n) + 5n = 30

Multiply (3 + 4n) * (-2 + 3n)
(3(-2 + 3n) + 4n * (-2 + 3n)) + 5n = 30
((-2 * 3 + 3n * 3) + 4n * (-2 + 3n)) + 5n = 30
((-6 + 9n) + 4n * (-2 + 3n)) + 5n = 30
(-6 + 9n + (-2 * 4n + 3n * 4n)) + 5n = 30
(-6 + 9n + (-8n + 12n2)) + 5n = 30

Combine like terms: 9n + -8n = 1n
(-6 + 1n + 12n2) + 5n = 30

Reorder the terms:
-6 + 1n + 5n + 12n2 = 30

Combine like terms: 1n + 5n = 6n
-6 + 6n + 12n2 = 30

Solving
-6 + 6n + 12n2 = 30

Solving for variable 'n'.

Reorder the terms:
-6 + -30 + 6n + 12n2 = 30 + -30

Combine like terms: -6 + -30 = -36
-36 + 6n + 12n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-36 + 6n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + n + 2n2) = 0

Factor a trinomial.
6((-2 + -1n)(3 + -2n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

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

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-2, 1.5}