(2x-4)(x+8)=(24)(42)

Solution for (2x-4)(x+8)=(24)(42) equation:

Simplifying
(2x + -4)(x + 8) = (24)(42)

Reorder the terms:
(-4 + 2x)(x + 8) = (24)(42)

Reorder the terms:
(-4 + 2x)(8 + x) = (24)(42)

Multiply (-4 + 2x) * (8 + x)
(-4(8 + x) + 2x * (8 + x)) = (24)(42)
((8 * -4 + x * -4) + 2x * (8 + x)) = (24)(42)
((-32 + -4x) + 2x * (8 + x)) = (24)(42)
(-32 + -4x + (8 * 2x + x * 2x)) = (24)(42)
(-32 + -4x + (16x + 2x2)) = (24)(42)

Combine like terms: -4x + 16x = 12x
(-32 + 12x + 2x2) = (24)(42)

Multiply 24 * 42
-32 + 12x + 2x2 = 1008

Solving
-32 + 12x + 2x2 = 1008

Solving for variable 'x'.

Reorder the terms:
-32 + -1008 + 12x + 2x2 = 1008 + -1008

Combine like terms: -32 + -1008 = -1040
-1040 + 12x + 2x2 = 1008 + -1008

Combine like terms: 1008 + -1008 = 0
-1040 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-520 + 6x + x2) = 0

Factor a trinomial.
2((-26 + -1x)(20 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve:

Simplifying
-26 + -1x = 0

Solving
-26 + -1x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -1x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1x = 0 + 26
-1x = 0 + 26

Combine like terms: 0 + 26 = 26
-1x = 26

Divide each side by '-1'.
x = -26

Simplifying
x = -26
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 = {-26, 20}