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

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


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

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

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

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

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

Solving
0 = 32 + -20x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -32 = -32
-32 + 20x + -3x2 = 32 + -20x + 3x2 + -32 + 20x + -3x2

Reorder the terms:
-32 + 20x + -3x2 = 32 + -32 + -20x + 20x + 3x2 + -3x2

Combine like terms: 32 + -32 = 0
-32 + 20x + -3x2 = 0 + -20x + 20x + 3x2 + -3x2
-32 + 20x + -3x2 = -20x + 20x + 3x2 + -3x2

Combine like terms: -20x + 20x = 0
-32 + 20x + -3x2 = 0 + 3x2 + -3x2
-32 + 20x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-32 + 20x + -3x2 = 0

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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