x^3+mx^2+nx-45=p

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Solution for x^3+mx^2+nx-45=p equation:


Simplifying
x3 + mx2 + nx + -45 = p

Reorder the terms:
-45 + mx2 + nx + x3 = p

Solving
-45 + mx2 + nx + x3 = p

Solving for variable 'm'.

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

Add '45' to each side of the equation.
-45 + mx2 + nx + 45 + x3 = 45 + p

Reorder the terms:
-45 + 45 + mx2 + nx + x3 = 45 + p

Combine like terms: -45 + 45 = 0
0 + mx2 + nx + x3 = 45 + p
mx2 + nx + x3 = 45 + p

Add '-1nx' to each side of the equation.
mx2 + nx + -1nx + x3 = 45 + -1nx + p

Combine like terms: nx + -1nx = 0
mx2 + 0 + x3 = 45 + -1nx + p
mx2 + x3 = 45 + -1nx + p

Add '-1x3' to each side of the equation.
mx2 + x3 + -1x3 = 45 + -1nx + p + -1x3

Combine like terms: x3 + -1x3 = 0
mx2 + 0 = 45 + -1nx + p + -1x3
mx2 = 45 + -1nx + p + -1x3

Divide each side by 'x2'.
m = 45x-2 + -1nx-1 + px-2 + -1x

Simplifying
m = 45x-2 + -1nx-1 + px-2 + -1x

Reorder the terms:
m = -1nx-1 + px-2 + 45x-2 + -1x

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