M^2+m(3m-4)=0

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Solution for M^2+m(3m-4)=0 equation: 


Simplifying
M2 + m(3m + -4) = 0

Reorder the terms:
M2 + m(-4 + 3m) = 0
M2 + (-4 * m + 3m * m) = 0
M2 + (-4m + 3m2) = 0

Solving
M2 + -4m + 3m2 = 0

Solving for variable 'M'.

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

Add '4m' to each side of the equation.
M2 + -4m + 4m + 3m2 = 0 + 4m

Combine like terms: -4m + 4m = 0
M2 + 0 + 3m2 = 0 + 4m
M2 + 3m2 = 0 + 4m
Remove the zero:
M2 + 3m2 = 4m

Add '-3m2' to each side of the equation.
M2 + 3m2 + -3m2 = 4m + -3m2

Combine like terms: 3m2 + -3m2 = 0
M2 + 0 = 4m + -3m2
M2 = 4m + -3m2

Simplifying
M2 = 4m + -3m2

Reorder the terms:
M2 + -4m + 3m2 = 4m + -4m + -3m2 + 3m2

Combine like terms: 4m + -4m = 0
M2 + -4m + 3m2 = 0 + -3m2 + 3m2
M2 + -4m + 3m2 = -3m2 + 3m2

Combine like terms: -3m2 + 3m2 = 0
M2 + -4m + 3m2 = 0

Factor a trinomial.
(M + -3m)(M + -1m) = 0


Subproblem 1
Set the factor '(M + -3m)' equal to zero and attempt to solve:

Simplifying
M + -3m = 0

Solving
M + -3m = 0

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

Add '3m' to each side of the equation.
M + -3m + 3m = 0 + 3m

Combine like terms: -3m + 3m = 0
M + 0 = 0 + 3m
M = 0 + 3m
Remove the zero:
M = 3m

Simplifying
M = 3m

Subproblem 2
Set the factor '(M + -1m)' equal to zero and attempt to solve:

Simplifying
M + -1m = 0

Solving
M + -1m = 0

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

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

Combine like terms: -1m + m = 0
M + 0 = 0 + m
M = 0 + m
Remove the zero:
M = m

Simplifying
M = m
Solution
M = {3m, m}

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