(x-3)*(x+8)=0

Solution for (x-3)*(x+8)=0 equation:

Simplifying
(x + -3)(x + 8) = 0

Reorder the terms:
(-3 + x)(x + 8) = 0

Reorder the terms:
(-3 + x)(8 + x) = 0

Multiply (-3 + x) * (8 + x)
(-3(8 + x) + x(8 + x)) = 0
((8 * -3 + x * -3) + x(8 + x)) = 0
((-24 + -3x) + x(8 + x)) = 0
(-24 + -3x + (8 * x + x * x)) = 0
(-24 + -3x + (8x + x2)) = 0

Combine like terms: -3x + 8x = 5x
(-24 + 5x + x2) = 0

Solving
-24 + 5x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-8, 3}