(3x-8)(4-x)=0

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Solution for (3x-8)(4-x)=0 equation: 


Simplifying
(3x + -8)(4 + -1x) = 0

Reorder the terms:
(-8 + 3x)(4 + -1x) = 0

Multiply (-8 + 3x) * (4 + -1x)
(-8(4 + -1x) + 3x * (4 + -1x)) = 0
((4 * -8 + -1x * -8) + 3x * (4 + -1x)) = 0
((-32 + 8x) + 3x * (4 + -1x)) = 0
(-32 + 8x + (4 * 3x + -1x * 3x)) = 0
(-32 + 8x + (12x + -3x2)) = 0

Combine like terms: 8x + 12x = 20x
(-32 + 20x + -3x2) = 0

Solving
-32 + 20x + -3x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {4, 2.666666667}

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