Mx^2+2Mx-x=0

Solution for Mx^2+2Mx-x=0 equation:

Simplifying
Mx2 + 2Mx + -1x = 0

Reorder the terms:
-1x + 2xM + x2M = 0

Solving
-1x + 2xM + x2M = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 2M + xM) = 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 '(-1 + 2M + xM)' equal to zero and attempt to solve:

Simplifying
-1 + 2M + xM = 0

Solving
-1 + 2M + xM = 0

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

Add '1' to each side of the equation.
-1 + 2M + 1 + xM = 0 + 1

Reorder the terms:
-1 + 1 + 2M + xM = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2M + xM = 0 + 1
2M + xM = 0 + 1

Combine like terms: 0 + 1 = 1
2M + xM = 1

Add '-2M' to each side of the equation.
2M + -2M + xM = 1 + -2M

Combine like terms: 2M + -2M = 0
0 + xM = 1 + -2M
xM = 1 + -2M

Divide each side by 'M'.
x = M-1 + -2

Simplifying
x = M-1 + -2

Reorder the terms:
x = -2 + M-1
Solution
x = {0, -2 + M-1}