(5m-5)(-3m+6)=0

Solution for (5m-5)(-3m+6)=0 equation:

Simplifying
(5m + -5)(-3m + 6) = 0

Reorder the terms:
(-5 + 5m)(-3m + 6) = 0

Reorder the terms:
(-5 + 5m)(6 + -3m) = 0

Multiply (-5 + 5m) * (6 + -3m)
(-5(6 + -3m) + 5m * (6 + -3m)) = 0
((6 * -5 + -3m * -5) + 5m * (6 + -3m)) = 0
((-30 + 15m) + 5m * (6 + -3m)) = 0
(-30 + 15m + (6 * 5m + -3m * 5m)) = 0
(-30 + 15m + (30m + -15m2)) = 0

Combine like terms: 15m + 30m = 45m
(-30 + 45m + -15m2) = 0

Solving
-30 + 45m + -15m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-2 + 3m + -1m2) = 0

Factor a trinomial.
15((-2 + m)(1 + -1m)) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-2 + m)' equal to zero and attempt to solve:

Simplifying
-2 + m = 0

Solving
-2 + m = 0

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

Add '2' to each side of the equation.
-2 + 2 + m = 0 + 2

Combine like terms: -2 + 2 = 0
0 + m = 0 + 2
m = 0 + 2

Combine like terms: 0 + 2 = 2
m = 2

Simplifying
m = 2
Subproblem 2
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 = {2, 1}