(3x-8)(x-3)=14

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Solution for (3x-8)(x-3)=14 equation: 


Simplifying
(3x + -8)(x + -3) = 14

Reorder the terms:
(-8 + 3x)(x + -3) = 14

Reorder the terms:
(-8 + 3x)(-3 + x) = 14

Multiply (-8 + 3x) * (-3 + x)
(-8(-3 + x) + 3x * (-3 + x)) = 14
((-3 * -8 + x * -8) + 3x * (-3 + x)) = 14
((24 + -8x) + 3x * (-3 + x)) = 14
(24 + -8x + (-3 * 3x + x * 3x)) = 14
(24 + -8x + (-9x + 3x2)) = 14

Combine like terms: -8x + -9x = -17x
(24 + -17x + 3x2) = 14

Solving
24 + -17x + 3x2 = 14

Solving for variable 'x'.

Reorder the terms:
24 + -14 + -17x + 3x2 = 14 + -14

Combine like terms: 24 + -14 = 10
10 + -17x + 3x2 = 14 + -14

Combine like terms: 14 + -14 = 0
10 + -17x + 3x2 = 0

Factor a trinomial.
(2 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0.6666666667, 5}

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