1008=(x+6)(2x-8)

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Solution for 1008=(x+6)(2x-8) equation: 


Simplifying
1008 = (x + 6)(2x + -8)

Reorder the terms:
1008 = (6 + x)(2x + -8)

Reorder the terms:
1008 = (6 + x)(-8 + 2x)

Multiply (6 + x) * (-8 + 2x)
1008 = (6(-8 + 2x) + x(-8 + 2x))
1008 = ((-8 * 6 + 2x * 6) + x(-8 + 2x))
1008 = ((-48 + 12x) + x(-8 + 2x))
1008 = (-48 + 12x + (-8 * x + 2x * x))
1008 = (-48 + 12x + (-8x + 2x2))

Combine like terms: 12x + -8x = 4x
1008 = (-48 + 4x + 2x2)

Solving
1008 = -48 + 4x + 2x2

Solving for variable 'x'.

Combine like terms: 1008 + 48 = 1056
1056 + -4x + -2x2 = -48 + 4x + 2x2 + 48 + -4x + -2x2

Reorder the terms:
1056 + -4x + -2x2 = -48 + 48 + 4x + -4x + 2x2 + -2x2

Combine like terms: -48 + 48 = 0
1056 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
1056 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
1056 + -4x + -2x2 = 0 + 2x2 + -2x2
1056 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1056 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(528 + -2x + -1x2) = 0

Factor a trinomial.
2((22 + -1x)(24 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22

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 = {22, -24}

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