4a^3+4a^2-80a=0 use factorization to solve for the unknown
First, we can factor out 4a:
4a(a^2 + a - 20) = 0
Now we can use the factoring technique known as "AC method" to factor the quadratic expression in parentheses. We need to find two numbers that multiply to -20 and add up to 1 (the coefficient of the "a" term):
a^2 + 5a - 4a - 20 = 0
(a^2 + 5a) - (4a + 20) = 0
a(a + 5) - 4(a + 5) = 0
(a + 5)(a - 4) = 0
Therefore, the solutions are:
a = -5 or a = 4
(Note that we must include the 0 solution from the factored equation as well).