(x-2)(3x-8)=16

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Solution for (x-2)(3x-8)=16 equation: 


Simplifying
(x + -2)(3x + -8) = 16

Reorder the terms:
(-2 + x)(3x + -8) = 16

Reorder the terms:
(-2 + x)(-8 + 3x) = 16

Multiply (-2 + x) * (-8 + 3x)
(-2(-8 + 3x) + x(-8 + 3x)) = 16
((-8 * -2 + 3x * -2) + x(-8 + 3x)) = 16
((16 + -6x) + x(-8 + 3x)) = 16
(16 + -6x + (-8 * x + 3x * x)) = 16
(16 + -6x + (-8x + 3x2)) = 16

Combine like terms: -6x + -8x = -14x
(16 + -14x + 3x2) = 16

Add '-16' to each side of the equation.
16 + -14x + -16 + 3x2 = 16 + -16

Reorder the terms:
16 + -16 + -14x + 3x2 = 16 + -16

Combine like terms: 16 + -16 = 0
0 + -14x + 3x2 = 16 + -16
-14x + 3x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-14x + 3x2 = 0

Solving
-14x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-14 + 3x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-14 + 3x)' equal to zero and attempt to solve:

Simplifying
-14 + 3x = 0

Solving
-14 + 3x = 0

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

Add '14' to each side of the equation.
-14 + 14 + 3x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3x = 0 + 14
3x = 0 + 14

Combine like terms: 0 + 14 = 14
3x = 14

Divide each side by '3'.
x = 4.666666667

Simplifying
x = 4.666666667
Solution
x = {0, 4.666666667}

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