(x+3)(x-4)=8

Solution for (x+3)(x-4)=8 equation:

Simplifying
(x + 3)(x + -4) = 8

Reorder the terms:
(3 + x)(x + -4) = 8

Reorder the terms:
(3 + x)(-4 + x) = 8

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) = 8
((-4 * 3 + x * 3) + x(-4 + x)) = 8
((-12 + 3x) + x(-4 + x)) = 8
(-12 + 3x + (-4 * x + x * x)) = 8
(-12 + 3x + (-4x + x2)) = 8

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) = 8

Solving
-12 + -1x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-12 + -8 + -1x + x2 = 8 + -8

Combine like terms: -12 + -8 = -20
-20 + -1x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-20 + -1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-4, 5}