x=-(x-3)(x-8)

Solution for x=-(x-3)(x-8) equation:

Simplifying
x = -1(x + -3)(x + -8)

Reorder the terms:
x = -1(-3 + x)(x + -8)

Reorder the terms:
x = -1(-3 + x)(-8 + x)

Multiply (-3 + x) * (-8 + x)
x = -1(-3(-8 + x) + x(-8 + x))
x = -1((-8 * -3 + x * -3) + x(-8 + x))
x = -1((24 + -3x) + x(-8 + x))
x = -1(24 + -3x + (-8 * x + x * x))
x = -1(24 + -3x + (-8x + x2))

Combine like terms: -3x + -8x = -11x
x = -1(24 + -11x + x2)
x = (24 * -1 + -11x * -1 + x2 * -1)
x = (-24 + 11x + -1x2)

Solving
x = -24 + 11x + -1x2

Solving for variable 'x'.

Reorder the terms:
24 + x + -11x + x2 = -24 + 11x + -1x2 + 24 + -11x + x2

Combine like terms: x + -11x = -10x
24 + -10x + x2 = -24 + 11x + -1x2 + 24 + -11x + x2

Reorder the terms:
24 + -10x + x2 = -24 + 24 + 11x + -11x + -1x2 + x2

Combine like terms: -24 + 24 = 0
24 + -10x + x2 = 0 + 11x + -11x + -1x2 + x2
24 + -10x + x2 = 11x + -11x + -1x2 + x2

Combine like terms: 11x + -11x = 0
24 + -10x + x2 = 0 + -1x2 + x2
24 + -10x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
24 + -10x + x2 = 0

Factor a trinomial.
(4 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}