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

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


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

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

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

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

Combine like terms: -8x + 3x = -5x
(-8 + -5x + 3x2) = (x + -4)(2x + -1)

Reorder the terms:
-8 + -5x + 3x2 = (-4 + x)(2x + -1)

Reorder the terms:
-8 + -5x + 3x2 = (-4 + x)(-1 + 2x)

Multiply (-4 + x) * (-1 + 2x)
-8 + -5x + 3x2 = (-4(-1 + 2x) + x(-1 + 2x))
-8 + -5x + 3x2 = ((-1 * -4 + 2x * -4) + x(-1 + 2x))
-8 + -5x + 3x2 = ((4 + -8x) + x(-1 + 2x))
-8 + -5x + 3x2 = (4 + -8x + (-1 * x + 2x * x))
-8 + -5x + 3x2 = (4 + -8x + (-1x + 2x2))

Combine like terms: -8x + -1x = -9x
-8 + -5x + 3x2 = (4 + -9x + 2x2)

Solving
-8 + -5x + 3x2 = 4 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + -4 + -5x + 9x + 3x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Combine like terms: -8 + -4 = -12
-12 + -5x + 9x + 3x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Combine like terms: -5x + 9x = 4x
-12 + 4x + 3x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-12 + 4x + 1x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Reorder the terms:
-12 + 4x + 1x2 = 4 + -4 + -9x + 9x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-12 + 4x + 1x2 = 0 + -9x + 9x + 2x2 + -2x2
-12 + 4x + 1x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
-12 + 4x + 1x2 = 0 + 2x2 + -2x2
-12 + 4x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + 4x + 1x2 = 0

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


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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
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
Solution
x = {-6, 2}

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