3x(x-3)=x-8

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


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

Reorder the terms:
3x(-3 + x) = x + -8
(-3 * 3x + x * 3x) = x + -8
(-9x + 3x2) = x + -8

Reorder the terms:
-9x + 3x2 = -8 + x

Solving
-9x + 3x2 = -8 + x

Solving for variable 'x'.

Reorder the terms:
8 + -9x + -1x + 3x2 = -8 + x + 8 + -1x

Combine like terms: -9x + -1x = -10x
8 + -10x + 3x2 = -8 + x + 8 + -1x

Reorder the terms:
8 + -10x + 3x2 = -8 + 8 + x + -1x

Combine like terms: -8 + 8 = 0
8 + -10x + 3x2 = 0 + x + -1x
8 + -10x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
8 + -10x + 3x2 = 0

Factor a trinomial.
(4 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
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
Solution
x = {1.333333333, 2}

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