Solve the equation. Show your work.
3m^2=-6m
To solve the equation 3m^2 = -6m, we can follow these steps:
Step 1: Move all the terms to one side of the equation to set it equal to zero:
3m^2 + 6m = 0
Step 2: Factor out the greatest common factor, which in this case is m:
m(3m + 6) = 0
Step 3: Apply the Zero Product Property, which states that if a product of factors equals zero, then at least one of the factors must be zero. Therefore, set each factor equal to zero and solve for m:
m = 0 OR 3m + 6 = 0
For the first factor, m = 0.
For the second factor, solve the equation 3m + 6 = 0:
Subtract 6 from both sides:
3m = -6
Divide both sides by 3:
m = -2
Therefore, the solution to the equation 3m^2 = -6m is m = 0 or m = -2.