=(7n+1)(8n+3)

Solution for =(7n+1)(8n+3) equation:

Simplifying
0 = (7n + 1)(8n + 3)

Reorder the terms:
0 = (1 + 7n)(8n + 3)

Reorder the terms:
0 = (1 + 7n)(3 + 8n)

Multiply (1 + 7n) * (3 + 8n)
0 = (1(3 + 8n) + 7n * (3 + 8n))
0 = ((3 * 1 + 8n * 1) + 7n * (3 + 8n))
0 = ((3 + 8n) + 7n * (3 + 8n))
0 = (3 + 8n + (3 * 7n + 8n * 7n))
0 = (3 + 8n + (21n + 56n2))

Combine like terms: 8n + 21n = 29n
0 = (3 + 29n + 56n2)

Solving
0 = 3 + 29n + 56n2

Solving for variable 'n'.

Combine like terms: 0 + -3 = -3
-3 + -29n + -56n2 = 3 + 29n + 56n2 + -3 + -29n + -56n2

Reorder the terms:
-3 + -29n + -56n2 = 3 + -3 + 29n + -29n + 56n2 + -56n2

Combine like terms: 3 + -3 = 0
-3 + -29n + -56n2 = 0 + 29n + -29n + 56n2 + -56n2
-3 + -29n + -56n2 = 29n + -29n + 56n2 + -56n2

Combine like terms: 29n + -29n = 0
-3 + -29n + -56n2 = 0 + 56n2 + -56n2
-3 + -29n + -56n2 = 56n2 + -56n2

Combine like terms: 56n2 + -56n2 = 0
-3 + -29n + -56n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 29n + 56n2) = 0

Factor a trinomial.
-1((3 + 8n)(1 + 7n)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 8n)' equal to zero and attempt to solve:

Simplifying
3 + 8n = 0

Solving
3 + 8n = 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 + 8n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8n = 0 + -3
8n = 0 + -3

Combine like terms: 0 + -3 = -3
8n = -3

Divide each side by '8'.
n = -0.375

Simplifying
n = -0.375
Subproblem 2
Set the factor '(1 + 7n)' equal to zero and attempt to solve:

Simplifying
1 + 7n = 0

Solving
1 + 7n = 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 + 7n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7n = 0 + -1
7n = 0 + -1

Combine like terms: 0 + -1 = -1
7n = -1

Divide each side by '7'.
n = -0.1428571429

Simplifying
n = -0.1428571429
Solution
n = {-0.375, -0.1428571429}