8(2-x)-3(x-1)(2-x)=0

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Solution for 8(2-x)-3(x-1)(2-x)=0 equation: 


Simplifying
8(2 + -1x) + -3(x + -1)(2 + -1x) = 0
(2 * 8 + -1x * 8) + -3(x + -1)(2 + -1x) = 0
(16 + -8x) + -3(x + -1)(2 + -1x) = 0

Reorder the terms:
16 + -8x + -3(-1 + x)(2 + -1x) = 0

Multiply (-1 + x) * (2 + -1x)
16 + -8x + -3(-1(2 + -1x) + x(2 + -1x)) = 0
16 + -8x + -3((2 * -1 + -1x * -1) + x(2 + -1x)) = 0
16 + -8x + -3((-2 + 1x) + x(2 + -1x)) = 0
16 + -8x + -3(-2 + 1x + (2 * x + -1x * x)) = 0
16 + -8x + -3(-2 + 1x + (2x + -1x2)) = 0

Combine like terms: 1x + 2x = 3x
16 + -8x + -3(-2 + 3x + -1x2) = 0
16 + -8x + (-2 * -3 + 3x * -3 + -1x2 * -3) = 0
16 + -8x + (6 + -9x + 3x2) = 0

Reorder the terms:
16 + 6 + -8x + -9x + 3x2 = 0

Combine like terms: 16 + 6 = 22
22 + -8x + -9x + 3x2 = 0

Combine like terms: -8x + -9x = -17x
22 + -17x + 3x2 = 0

Solving
22 + -17x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(11 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {2, 3.666666667}

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