M^2-2M+3M^2+M=

Solution for M^2-2M+3M^2+M= equation:

Simplifying
M2 + -2M + 3M2 + M = 0

Reorder the terms:
-2M + M + M2 + 3M2 = 0

Combine like terms: -2M + M = -1M
-1M + M2 + 3M2 = 0

Combine like terms: M2 + 3M2 = 4M2
-1M + 4M2 = 0

Solving
-1M + 4M2 = 0

Solving for variable 'M'.

Factor out the Greatest Common Factor (GCF), 'M'.
M(-1 + 4M) = 0

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

Simplifying
M = 0

Solving
M = 0

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

Simplifying
M = 0
Subproblem 2
Set the factor '(-1 + 4M)' equal to zero and attempt to solve:

Simplifying
-1 + 4M = 0

Solving
-1 + 4M = 0

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

Add '1' to each side of the equation.
-1 + 1 + 4M = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4M = 0 + 1
4M = 0 + 1

Combine like terms: 0 + 1 = 1
4M = 1

Divide each side by '4'.
M = 0.25

Simplifying
M = 0.25
Solution
M = {0, 0.25}