x^3+mx^2+nx+6=0

Solution for x^3+mx^2+nx+6=0 equation:

Simplifying
x3 + mx2 + nx + 6 = 0

Reorder the terms:
6 + mx2 + nx + x3 = 0

Solving
6 + mx2 + nx + x3 = 0

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + mx2 + nx + -6 + x3 = 0 + -6

Reorder the terms:
6 + -6 + mx2 + nx + x3 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + mx2 + nx + x3 = 0 + -6
mx2 + nx + x3 = 0 + -6

Combine like terms: 0 + -6 = -6
mx2 + nx + x3 = -6

Add '-1nx' to each side of the equation.
mx2 + nx + -1nx + x3 = -6 + -1nx

Combine like terms: nx + -1nx = 0
mx2 + 0 + x3 = -6 + -1nx
mx2 + x3 = -6 + -1nx

Add '-1x3' to each side of the equation.
mx2 + x3 + -1x3 = -6 + -1nx + -1x3

Combine like terms: x3 + -1x3 = 0
mx2 + 0 = -6 + -1nx + -1x3
mx2 = -6 + -1nx + -1x3

Divide each side by 'x2'.
m = -6x-2 + -1nx-1 + -1x

Simplifying
m = -6x-2 + -1nx-1 + -1x

Reorder the terms:
m = -1nx-1 + -6x-2 + -1x