To solve each equation, we need to first simplify or rearrange the equation to isolate the variable. Then, we can solve for the variable.

1) 14x - x² = 48
Rearranging the equation:
x² - 14x + 48 = 0
Solving for x:
This is a quadratic equation, so we can factor it to get two solutions:
(x - 6)(x - 8) = 0
Setting each factor to zero:
x - 6 = 0 or x - 8 = 0
x = 6 or x = 8

2) 6x - 1 = 9x²
Rearranging the equation:
9x² - 6x + 1 = 0
This is also a quadratic equation:
Solving for x:
Using the quadratic formula:
x = [6 ± sqrt((-6)² - 491)] / (2*9)
x = [6 ± sqrt(36 - 36)] / 18
x = [6 ± 0] / 18
x = 6 / 18
x = 1/3

3) 6x² + 3 = -7x
Rearranging the equation:
6x² + 7x + 3 = 0
This is a quadratic equation:
Solving for x:
Using the quadratic formula:
x = [-7 ± sqrt(7² - 463)] / (2*6)
x = [-7 ± sqrt(49 - 72)] / 12
x = [-7 ± sqrt(-23)] / 12
This equation has complex solutions.

4) 19x - 14 - 6x² = 0
Rearranging the equation:
6x² - 19x + 14 = 0
This is a quadratic equation:
Solving for x:
This can be factored to:
(3x - 2)(2x - 7) = 0
Setting each factor to zero:
3x - 2 = 0 or 2x - 7 = 0
x = 2/3 or x = 7/2

5) n² = 11n - 10
Rearranging the equation:
n² - 11n + 10 = 0
Solving for n:
This can be factored to:
(n - 10)(n - 1) = 0
Setting each factor to zero:
n - 10 = 0 or n - 1 = 0
n = 10 or n = 1

6) x² = 4x
Rearranging the equation:
x² - 4x = 0
Solving for x:
This can be factored to:
x(x - 4) = 0
Setting each factor to zero:
x = 0 or x - 4 = 0
x = 0 or x = 4

These are the solutions for each of the given equations.