(10-x)(x+6)=0

Solution for (10-x)(x+6)=0 equation:

Simplifying
(10 + -1x)(x + 6) = 0

Reorder the terms:
(10 + -1x)(6 + x) = 0

Multiply (10 + -1x) * (6 + x)
(10(6 + x) + -1x * (6 + x)) = 0
((6 * 10 + x * 10) + -1x * (6 + x)) = 0
((60 + 10x) + -1x * (6 + x)) = 0
(60 + 10x + (6 * -1x + x * -1x)) = 0
(60 + 10x + (-6x + -1x2)) = 0

Combine like terms: 10x + -6x = 4x
(60 + 4x + -1x2) = 0

Solving
60 + 4x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + -1x)(6 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {10, -6}