(3x-4)(x-8)=(x-6)(4x-5)

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Solution for (3x-4)(x-8)=(x-6)(4x-5) equation: 


Simplifying
(3x + -4)(x + -8) = (x + -6)(4x + -5)

Reorder the terms:
(-4 + 3x)(x + -8) = (x + -6)(4x + -5)

Reorder the terms:
(-4 + 3x)(-8 + x) = (x + -6)(4x + -5)

Multiply (-4 + 3x) * (-8 + x)
(-4(-8 + x) + 3x * (-8 + x)) = (x + -6)(4x + -5)
((-8 * -4 + x * -4) + 3x * (-8 + x)) = (x + -6)(4x + -5)
((32 + -4x) + 3x * (-8 + x)) = (x + -6)(4x + -5)
(32 + -4x + (-8 * 3x + x * 3x)) = (x + -6)(4x + -5)
(32 + -4x + (-24x + 3x2)) = (x + -6)(4x + -5)

Combine like terms: -4x + -24x = -28x
(32 + -28x + 3x2) = (x + -6)(4x + -5)

Reorder the terms:
32 + -28x + 3x2 = (-6 + x)(4x + -5)

Reorder the terms:
32 + -28x + 3x2 = (-6 + x)(-5 + 4x)

Multiply (-6 + x) * (-5 + 4x)
32 + -28x + 3x2 = (-6(-5 + 4x) + x(-5 + 4x))
32 + -28x + 3x2 = ((-5 * -6 + 4x * -6) + x(-5 + 4x))
32 + -28x + 3x2 = ((30 + -24x) + x(-5 + 4x))
32 + -28x + 3x2 = (30 + -24x + (-5 * x + 4x * x))
32 + -28x + 3x2 = (30 + -24x + (-5x + 4x2))

Combine like terms: -24x + -5x = -29x
32 + -28x + 3x2 = (30 + -29x + 4x2)

Solving
32 + -28x + 3x2 = 30 + -29x + 4x2

Solving for variable 'x'.

Reorder the terms:
32 + -30 + -28x + 29x + 3x2 + -4x2 = 30 + -29x + 4x2 + -30 + 29x + -4x2

Combine like terms: 32 + -30 = 2
2 + -28x + 29x + 3x2 + -4x2 = 30 + -29x + 4x2 + -30 + 29x + -4x2

Combine like terms: -28x + 29x = 1x
2 + 1x + 3x2 + -4x2 = 30 + -29x + 4x2 + -30 + 29x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
2 + 1x + -1x2 = 30 + -29x + 4x2 + -30 + 29x + -4x2

Reorder the terms:
2 + 1x + -1x2 = 30 + -30 + -29x + 29x + 4x2 + -4x2

Combine like terms: 30 + -30 = 0
2 + 1x + -1x2 = 0 + -29x + 29x + 4x2 + -4x2
2 + 1x + -1x2 = -29x + 29x + 4x2 + -4x2

Combine like terms: -29x + 29x = 0
2 + 1x + -1x2 = 0 + 4x2 + -4x2
2 + 1x + -1x2 = 4x2 + -4x2

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

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


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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {2, -1}

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