(x+3)(4x-8)=0

Solution for (x+3)(4x-8)=0 equation:

Simplifying
(x + 3)(4x + -8) = 0

Reorder the terms:
(3 + x)(4x + -8) = 0

Reorder the terms:
(3 + x)(-8 + 4x) = 0

Multiply (3 + x) * (-8 + 4x)
(3(-8 + 4x) + x(-8 + 4x)) = 0
((-8 * 3 + 4x * 3) + x(-8 + 4x)) = 0
((-24 + 12x) + x(-8 + 4x)) = 0
(-24 + 12x + (-8 * x + 4x * x)) = 0
(-24 + 12x + (-8x + 4x2)) = 0

Combine like terms: 12x + -8x = 4x
(-24 + 4x + 4x2) = 0

Solving
-24 + 4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 4.
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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}