m^2(7m+1)=8m

Solution for m^2(7m+1)=8m equation:

Simplifying
m2(7m + 1) = 8m

Reorder the terms:
m2(1 + 7m) = 8m
(1 * m2 + 7m * m2) = 8m
(1m2 + 7m3) = 8m

Solving
1m2 + 7m3 = 8m

Solving for variable 'm'.

Reorder the terms:
-8m + 1m2 + 7m3 = 8m + -8m

Combine like terms: 8m + -8m = 0
-8m + 1m2 + 7m3 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-8 + m + 7m2) = 0

Factor a trinomial.
m((-8 + -7m)(1 + -1m)) = 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 '(-8 + -7m)' equal to zero and attempt to solve:

Simplifying
-8 + -7m = 0

Solving
-8 + -7m = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7m = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7m = 0 + 8
-7m = 0 + 8

Combine like terms: 0 + 8 = 8
-7m = 8

Divide each side by '-7'.
m = -1.142857143

Simplifying
m = -1.142857143
Subproblem 3
Set the factor '(1 + -1m)' equal to zero and attempt to solve:

Simplifying
1 + -1m = 0

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

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

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

Divide each side by '-1'.
m = 1

Simplifying
m = 1
Solution
m = {0, -1.142857143, 1}