4((-24+-1x)(3+-1x))=0

Solution for 4((-24+-1x)(3+-1x))=0 equation:

Simplifying
4((-24 + -1x)(3 + -1x)) = 0

Multiply (-24 + -1x) * (3 + -1x)
4((-24(3 + -1x) + -1x * (3 + -1x))) = 0
4(((3 * -24 + -1x * -24) + -1x * (3 + -1x))) = 0
4(((-72 + 24x) + -1x * (3 + -1x))) = 0
4((-72 + 24x + (3 * -1x + -1x * -1x))) = 0
4((-72 + 24x + (-3x + 1x2))) = 0

Combine like terms: 24x + -3x = 21x
4((-72 + 21x + 1x2)) = 0
(-72 * 4 + 21x * 4 + 1x2 * 4) = 0
(-288 + 84x + 4x2) = 0

Solving
-288 + 84x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-72 + 21x + x2) = 0

Factor a trinomial.
4((-24 + -1x)(3 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

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

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

Divide each side by '-1'.
x = -24

Simplifying
x = -24
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 = {-24, 3}