P(x)=x^2-6x

Solution for P(x)=x^2-6x equation:

Simplifying
P(x) = x2 + -6x

Multiply P * x
xP = x2 + -6x

Reorder the terms:
xP = -6x + x2

Solving
xP = -6x + x2

Solving for variable 'x'.

Reorder the terms:
6x + xP + -1x2 = -6x + x2 + 6x + -1x2

Reorder the terms:
6x + xP + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
6x + xP + -1x2 = 0 + x2 + -1x2
6x + xP + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6x + xP + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + P + -1x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(6 + P + -1x)' equal to zero and attempt to solve:

Simplifying
6 + P + -1x = 0

Solving
6 + P + -1x = 0

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

Add '-6' to each side of the equation.
6 + P + -6 + -1x = 0 + -6

Reorder the terms:
6 + -6 + P + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + P + -1x = 0 + -6
P + -1x = 0 + -6

Combine like terms: 0 + -6 = -6
P + -1x = -6

Add '-1P' to each side of the equation.
P + -1P + -1x = -6 + -1P

Combine like terms: P + -1P = 0
0 + -1x = -6 + -1P
-1x = -6 + -1P

Divide each side by '-1'.
x = 6 + P

Simplifying
x = 6 + P
Solution
x = {0, 6 + P}