(x^2+x)(x-10)=0

Solution for (x^2+x)(x-10)=0 equation:

Simplifying
(x2 + x)(x + -10) = 0

Reorder the terms:
(x + x2)(x + -10) = 0

Reorder the terms:
(x + x2)(-10 + x) = 0

Multiply (x + x2) * (-10 + x)
(x(-10 + x) + x2(-10 + x)) = 0
((-10 * x + x * x) + x2(-10 + x)) = 0
((-10x + x2) + x2(-10 + x)) = 0
(-10x + x2 + (-10 * x2 + x * x2)) = 0
(-10x + x2 + (-10x2 + x3)) = 0

Combine like terms: x2 + -10x2 = -9x2
(-10x + -9x2 + x3) = 0

Solving
-10x + -9x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + -9x + x2) = 0

Factor a trinomial.
x((-1 + -1x)(10 + -1x)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 3
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0, -1, 10}