Solve equation x^3 + x^2 = 0?

x³ + x² = 0

So first you factor out an x²:
x²(x + 1) = 0

So now you set both equal to zero:
x² = 0............x + 1 = 0
x = 0..............x = -1

So:
x = 0 and -1 <==answer

x^3 + x^2 = 0
x^2(x + 1) = 0

x^2 = 0
x = 0

x + 1 = 0
x = -1

∴ x = -1, 0

x^3=-x^2
x=0
and
x=-1

First, factor out an x^2.

so you have: x^2(x+1) = 0

Since the left side is multiplied together and the right is a zero, we know that one of the terms from the left side is zero. So we can write 2 equations.

x^2 = 0 or x + 1 = 0.

sqrt(x^2) = 0
x = 0 or x = -1


Those are your two final answers.

0 and -1

0^3 + 0^2 = 0 + 0 = 0

-1^3 + -1^2 = -1 + 1 = 0

x^3 + x^2 = 0?

Factor and use the distributive law

x*x*x + x*x = 0
x*x*(x + 1) = 0

There are only 2 ways that this product can be 0
x = 0, since 0*0*(1) = 0
x = -1 since (-1)*(-1)*0 = 0

Your 3 solutions are 0,0,-1 since every cubic equation has 3 solutions.