(2x-4)(x+6)=(24)(39)

Solution for (2x-4)(x+6)=(24)(39) equation:

Simplifying
(2x + -4)(x + 6) = (24)(39)

Reorder the terms:
(-4 + 2x)(x + 6) = (24)(39)

Reorder the terms:
(-4 + 2x)(6 + x) = (24)(39)

Multiply (-4 + 2x) * (6 + x)
(-4(6 + x) + 2x * (6 + x)) = (24)(39)
((6 * -4 + x * -4) + 2x * (6 + x)) = (24)(39)
((-24 + -4x) + 2x * (6 + x)) = (24)(39)
(-24 + -4x + (6 * 2x + x * 2x)) = (24)(39)
(-24 + -4x + (12x + 2x2)) = (24)(39)

Combine like terms: -4x + 12x = 8x
(-24 + 8x + 2x2) = (24)(39)

Multiply 24 * 39
-24 + 8x + 2x2 = 936

Solving
-24 + 8x + 2x2 = 936

Solving for variable 'x'.

Reorder the terms:
-24 + -936 + 8x + 2x2 = 936 + -936

Combine like terms: -24 + -936 = -960
-960 + 8x + 2x2 = 936 + -936

Combine like terms: 936 + -936 = 0
-960 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-480 + 4x + x2) = 0

Factor a trinomial.
2((-24 + -1x)(20 + -1x)) = 0

Ignore the factor 2.
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 '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

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

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

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-24, 20}