6m(m-2)+3(m^2-7)=

Solution for 6m(m-2)+3(m^2-7)= equation:

Simplifying
6m(m + -2) + 3(m2 + -7) = 0

Reorder the terms:
6m(-2 + m) + 3(m2 + -7) = 0
(-2 * 6m + m * 6m) + 3(m2 + -7) = 0
(-12m + 6m2) + 3(m2 + -7) = 0

Reorder the terms:
-12m + 6m2 + 3(-7 + m2) = 0
-12m + 6m2 + (-7 * 3 + m2 * 3) = 0
-12m + 6m2 + (-21 + 3m2) = 0

Reorder the terms:
-21 + -12m + 6m2 + 3m2 = 0

Combine like terms: 6m2 + 3m2 = 9m2
-21 + -12m + 9m2 = 0

Solving
-21 + -12m + 9m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -4m + 3m2) = 0

Factor a trinomial.
3((-1 + -1m)(7 + -3m)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(7 + -3m)' equal to zero and attempt to solve:

Simplifying
7 + -3m = 0

Solving
7 + -3m = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3m = 0 + -7
-3m = 0 + -7

Combine like terms: 0 + -7 = -7
-3m = -7

Divide each side by '-3'.
m = 2.333333333

Simplifying
m = 2.333333333
Solution
m = {-1, 2.333333333}