(x-8)(4x-5)=(x+4)(1-2x)

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Solution for (x-8)(4x-5)=(x+4)(1-2x) equation: 


Simplifying
(x + -8)(4x + -5) = (x + 4)(1 + -2x)

Reorder the terms:
(-8 + x)(4x + -5) = (x + 4)(1 + -2x)

Reorder the terms:
(-8 + x)(-5 + 4x) = (x + 4)(1 + -2x)

Multiply (-8 + x) * (-5 + 4x)
(-8(-5 + 4x) + x(-5 + 4x)) = (x + 4)(1 + -2x)
((-5 * -8 + 4x * -8) + x(-5 + 4x)) = (x + 4)(1 + -2x)
((40 + -32x) + x(-5 + 4x)) = (x + 4)(1 + -2x)
(40 + -32x + (-5 * x + 4x * x)) = (x + 4)(1 + -2x)
(40 + -32x + (-5x + 4x2)) = (x + 4)(1 + -2x)

Combine like terms: -32x + -5x = -37x
(40 + -37x + 4x2) = (x + 4)(1 + -2x)

Reorder the terms:
40 + -37x + 4x2 = (4 + x)(1 + -2x)

Multiply (4 + x) * (1 + -2x)
40 + -37x + 4x2 = (4(1 + -2x) + x(1 + -2x))
40 + -37x + 4x2 = ((1 * 4 + -2x * 4) + x(1 + -2x))
40 + -37x + 4x2 = ((4 + -8x) + x(1 + -2x))
40 + -37x + 4x2 = (4 + -8x + (1 * x + -2x * x))
40 + -37x + 4x2 = (4 + -8x + (1x + -2x2))

Combine like terms: -8x + 1x = -7x
40 + -37x + 4x2 = (4 + -7x + -2x2)

Solving
40 + -37x + 4x2 = 4 + -7x + -2x2

Solving for variable 'x'.

Reorder the terms:
40 + -4 + -37x + 7x + 4x2 + 2x2 = 4 + -7x + -2x2 + -4 + 7x + 2x2

Combine like terms: 40 + -4 = 36
36 + -37x + 7x + 4x2 + 2x2 = 4 + -7x + -2x2 + -4 + 7x + 2x2

Combine like terms: -37x + 7x = -30x
36 + -30x + 4x2 + 2x2 = 4 + -7x + -2x2 + -4 + 7x + 2x2

Combine like terms: 4x2 + 2x2 = 6x2
36 + -30x + 6x2 = 4 + -7x + -2x2 + -4 + 7x + 2x2

Reorder the terms:
36 + -30x + 6x2 = 4 + -4 + -7x + 7x + -2x2 + 2x2

Combine like terms: 4 + -4 = 0
36 + -30x + 6x2 = 0 + -7x + 7x + -2x2 + 2x2
36 + -30x + 6x2 = -7x + 7x + -2x2 + 2x2

Combine like terms: -7x + 7x = 0
36 + -30x + 6x2 = 0 + -2x2 + 2x2
36 + -30x + 6x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
36 + -30x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -5x + x2) = 0

Factor a trinomial.
6((2 + -1x)(3 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
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
Solution
x = {2, 3}

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