10x+x(x-5)=

Solution for 10x+x(x-5)= equation:

Simplifying
10x + x(x + -5) = 0

Reorder the terms:
10x + x(-5 + x) = 0
10x + (-5 * x + x * x) = 0
10x + (-5x + x2) = 0

Combine like terms: 10x + -5x = 5x
5x + x2 = 0

Solving
5x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {0, -5}