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

Solution for (x-10)(x+1)=0 equation:

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

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

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

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

Combine like terms: -10x + 1x = -9x
(-10 + -9x + x2) = 0

Solving
-10 + -9x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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 2
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 = {-1, 10}