(x-4)(8x+2)=-22(x-4)

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Solution for (x-4)(8x+2)=-22(x-4) equation: 


Simplifying
(x + -4)(8x + 2) = -22(x + -4)

Reorder the terms:
(-4 + x)(8x + 2) = -22(x + -4)

Reorder the terms:
(-4 + x)(2 + 8x) = -22(x + -4)

Multiply (-4 + x) * (2 + 8x)
(-4(2 + 8x) + x(2 + 8x)) = -22(x + -4)
((2 * -4 + 8x * -4) + x(2 + 8x)) = -22(x + -4)
((-8 + -32x) + x(2 + 8x)) = -22(x + -4)
(-8 + -32x + (2 * x + 8x * x)) = -22(x + -4)
(-8 + -32x + (2x + 8x2)) = -22(x + -4)

Combine like terms: -32x + 2x = -30x
(-8 + -30x + 8x2) = -22(x + -4)

Reorder the terms:
-8 + -30x + 8x2 = -22(-4 + x)
-8 + -30x + 8x2 = (-4 * -22 + x * -22)
-8 + -30x + 8x2 = (88 + -22x)

Solving
-8 + -30x + 8x2 = 88 + -22x

Solving for variable 'x'.

Reorder the terms:
-8 + -88 + -30x + 22x + 8x2 = 88 + -22x + -88 + 22x

Combine like terms: -8 + -88 = -96
-96 + -30x + 22x + 8x2 = 88 + -22x + -88 + 22x

Combine like terms: -30x + 22x = -8x
-96 + -8x + 8x2 = 88 + -22x + -88 + 22x

Reorder the terms:
-96 + -8x + 8x2 = 88 + -88 + -22x + 22x

Combine like terms: 88 + -88 = 0
-96 + -8x + 8x2 = 0 + -22x + 22x
-96 + -8x + 8x2 = -22x + 22x

Combine like terms: -22x + 22x = 0
-96 + -8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-12 + -1x + x2) = 0

Factor a trinomial.
8((-3 + -1x)(4 + -1x)) = 0

Ignore the factor 8.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}

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