(x-8)(4x-3)=(x+6)(1-2x)

Solution for (x-8)(4x-3)=(x+6)(1-2x) equation:

Simplifying
(x + -8)(4x + -3) = (x + 6)(1 + -2x)

Reorder the terms:
(-8 + x)(4x + -3) = (x + 6)(1 + -2x)

Reorder the terms:
(-8 + x)(-3 + 4x) = (x + 6)(1 + -2x)

Multiply (-8 + x) * (-3 + 4x)
(-8(-3 + 4x) + x(-3 + 4x)) = (x + 6)(1 + -2x)
((-3 * -8 + 4x * -8) + x(-3 + 4x)) = (x + 6)(1 + -2x)
((24 + -32x) + x(-3 + 4x)) = (x + 6)(1 + -2x)
(24 + -32x + (-3 * x + 4x * x)) = (x + 6)(1 + -2x)
(24 + -32x + (-3x + 4x2)) = (x + 6)(1 + -2x)

Combine like terms: -32x + -3x = -35x
(24 + -35x + 4x2) = (x + 6)(1 + -2x)

Reorder the terms:
24 + -35x + 4x2 = (6 + x)(1 + -2x)

Multiply (6 + x) * (1 + -2x)
24 + -35x + 4x2 = (6(1 + -2x) + x(1 + -2x))
24 + -35x + 4x2 = ((1 * 6 + -2x * 6) + x(1 + -2x))
24 + -35x + 4x2 = ((6 + -12x) + x(1 + -2x))
24 + -35x + 4x2 = (6 + -12x + (1 * x + -2x * x))
24 + -35x + 4x2 = (6 + -12x + (1x + -2x2))

Combine like terms: -12x + 1x = -11x
24 + -35x + 4x2 = (6 + -11x + -2x2)

Solving
24 + -35x + 4x2 = 6 + -11x + -2x2

Solving for variable 'x'.

Reorder the terms:
24 + -6 + -35x + 11x + 4x2 + 2x2 = 6 + -11x + -2x2 + -6 + 11x + 2x2

Combine like terms: 24 + -6 = 18
18 + -35x + 11x + 4x2 + 2x2 = 6 + -11x + -2x2 + -6 + 11x + 2x2

Combine like terms: -35x + 11x = -24x
18 + -24x + 4x2 + 2x2 = 6 + -11x + -2x2 + -6 + 11x + 2x2

Combine like terms: 4x2 + 2x2 = 6x2
18 + -24x + 6x2 = 6 + -11x + -2x2 + -6 + 11x + 2x2

Reorder the terms:
18 + -24x + 6x2 = 6 + -6 + -11x + 11x + -2x2 + 2x2

Combine like terms: 6 + -6 = 0
18 + -24x + 6x2 = 0 + -11x + 11x + -2x2 + 2x2
18 + -24x + 6x2 = -11x + 11x + -2x2 + 2x2

Combine like terms: -11x + 11x = 0
18 + -24x + 6x2 = 0 + -2x2 + 2x2
18 + -24x + 6x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
18 + -24x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -4x + x2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
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 = {1, 3}