m(m+7)=78m^2

Solution for m(m+7)=78m^2 equation:

Simplifying
m(m + 7) = 78m2

Reorder the terms:
m(7 + m) = 78m2
(7 * m + m * m) = 78m2
(7m + m2) = 78m2

Solving
7m + m2 = 78m2

Solving for variable 'm'.

Combine like terms: m2 + -78m2 = -77m2
7m + -77m2 = 78m2 + -78m2

Combine like terms: 78m2 + -78m2 = 0
7m + -77m2 = 0

Factor out the Greatest Common Factor (GCF), '7m'.
7m(1 + -11m) = 0

Ignore the factor 7.
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 + -11m)' equal to zero and attempt to solve:

Simplifying
1 + -11m = 0

Solving
1 + -11m = 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 + -11m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -11m = 0 + -1
-11m = 0 + -1

Combine like terms: 0 + -1 = -1
-11m = -1

Divide each side by '-11'.
m = 0.09090909091

Simplifying
m = 0.09090909091
Solution
m = {0, 0.09090909091}