Solve the equation. Show your work.
3m^2=-6m
-6m=3.m.m
-6/3=m.m/m
-2=m
almost, but only partway:
3m^2 = -6m
3m^2 + 6m = 0
3m(m+2) = 0
a product is zero when any factor is zero
so, m=0 or -2
To solve the equation 3m^2 = -6m, you can follow these steps:
Step 1: Bring all the terms to one side of the equation, so that the equation is expressed in the form of a quadratic equation (ax^2 + bx + c = 0). In this case, we can subtract -6m from both sides, so the equation becomes:
3m^2 + 6m = 0
Step 2: Factor out the common term, m, from the left side of the equation:
m(3m + 6) = 0
Step 3: Apply the zero product property, which states that if a product of two factors equals zero, then at least one of the factors must be zero. Hence, set each factor equal to zero and solve for m:
m = 0 (By setting the first factor, m, equal to zero)
3m + 6 = 0 (By setting the second factor, 3m + 6, equal to zero)
Step 4: Solve the second equation by isolating m:
3m + 6 = 0 ==> 3m = -6 ==> m = -6/3 ==> m = -2
So, the solutions to the equation 3m^2 = -6m are m = 0 and m = -2.