4+5+4n=2(n+1)(4n-3)

Solution for 4+5+4n=2(n+1)(4n-3) equation:

Simplifying
4 + 5 + 4n = 2(n + 1)(4n + -3)

Combine like terms: 4 + 5 = 9
9 + 4n = 2(n + 1)(4n + -3)

Reorder the terms:
9 + 4n = 2(1 + n)(4n + -3)

Reorder the terms:
9 + 4n = 2(1 + n)(-3 + 4n)

Multiply (1 + n) * (-3 + 4n)
9 + 4n = 2(1(-3 + 4n) + n(-3 + 4n))
9 + 4n = 2((-3 * 1 + 4n * 1) + n(-3 + 4n))
9 + 4n = 2((-3 + 4n) + n(-3 + 4n))
9 + 4n = 2(-3 + 4n + (-3 * n + 4n * n))
9 + 4n = 2(-3 + 4n + (-3n + 4n2))

Combine like terms: 4n + -3n = 1n
9 + 4n = 2(-3 + 1n + 4n2)
9 + 4n = (-3 * 2 + 1n * 2 + 4n2 * 2)
9 + 4n = (-6 + 2n + 8n2)

Solving
9 + 4n = -6 + 2n + 8n2

Solving for variable 'n'.

Reorder the terms:
9 + 6 + 4n + -2n + -8n2 = -6 + 2n + 8n2 + 6 + -2n + -8n2

Combine like terms: 9 + 6 = 15
15 + 4n + -2n + -8n2 = -6 + 2n + 8n2 + 6 + -2n + -8n2

Combine like terms: 4n + -2n = 2n
15 + 2n + -8n2 = -6 + 2n + 8n2 + 6 + -2n + -8n2

Reorder the terms:
15 + 2n + -8n2 = -6 + 6 + 2n + -2n + 8n2 + -8n2

Combine like terms: -6 + 6 = 0
15 + 2n + -8n2 = 0 + 2n + -2n + 8n2 + -8n2
15 + 2n + -8n2 = 2n + -2n + 8n2 + -8n2

Combine like terms: 2n + -2n = 0
15 + 2n + -8n2 = 0 + 8n2 + -8n2
15 + 2n + -8n2 = 8n2 + -8n2

Combine like terms: 8n2 + -8n2 = 0
15 + 2n + -8n2 = 0

Factor a trinomial.
(3 + -2n)(5 + 4n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + 4n)' equal to zero and attempt to solve:

Simplifying
5 + 4n = 0

Solving
5 + 4n = 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 + 4n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4n = 0 + -5
4n = 0 + -5

Combine like terms: 0 + -5 = -5
4n = -5

Divide each side by '4'.
n = -1.25

Simplifying
n = -1.25
Solution
n = {1.5, -1.25}