=(x-3)(x+8)

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


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

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

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

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

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

Solving
0 = -24 + 5x + x2

Solving for variable 'x'.

Combine like terms: 0 + 24 = 24
24 + -5x + -1x2 = -24 + 5x + x2 + 24 + -5x + -1x2

Reorder the terms:
24 + -5x + -1x2 = -24 + 24 + 5x + -5x + x2 + -1x2

Combine like terms: -24 + 24 = 0
24 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2
24 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
24 + -5x + -1x2 = 0 + x2 + -1x2
24 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + -5x + -1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 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 + x = 0 + -8

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

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

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

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