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

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


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

Multiply 24 * 39
936 = (2x + -4)(x + 6)

Reorder the terms:
936 = (-4 + 2x)(x + 6)

Reorder the terms:
936 = (-4 + 2x)(6 + x)

Multiply (-4 + 2x) * (6 + x)
936 = (-4(6 + x) + 2x * (6 + x))
936 = ((6 * -4 + x * -4) + 2x * (6 + x))
936 = ((-24 + -4x) + 2x * (6 + x))
936 = (-24 + -4x + (6 * 2x + x * 2x))
936 = (-24 + -4x + (12x + 2x2))

Combine like terms: -4x + 12x = 8x
936 = (-24 + 8x + 2x2)

Solving
936 = -24 + 8x + 2x2

Solving for variable 'x'.

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

Reorder the terms:
960 + -8x + -2x2 = -24 + 24 + 8x + -8x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
960 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
960 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(480 + -4x + -1x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(24 + x)' equal to zero and attempt to solve:

Simplifying
24 + x = 0

Solving
24 + x = 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 + x = 0 + -24

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

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

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

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