3a(2-a)=8-a

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Solution for 3a(2-a)=8-a equation: 


Simplifying
3a(2 + -1a) = 8 + -1a
(2 * 3a + -1a * 3a) = 8 + -1a
(6a + -3a2) = 8 + -1a

Solving
6a + -3a2 = 8 + -1a

Solving for variable 'a'.

Reorder the terms:
-8 + 6a + a + -3a2 = 8 + -1a + -8 + a

Combine like terms: 6a + a = 7a
-8 + 7a + -3a2 = 8 + -1a + -8 + a

Reorder the terms:
-8 + 7a + -3a2 = 8 + -8 + -1a + a

Combine like terms: 8 + -8 = 0
-8 + 7a + -3a2 = 0 + -1a + a
-8 + 7a + -3a2 = -1a + a

Combine like terms: -1a + a = 0
-8 + 7a + -3a2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
2.666666667 + -2.333333333a + a2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.333333333a + -2.666666667 + a2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -2.333333333a + a2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -2.333333333a + a2 = 0 + -2.666666667
-2.333333333a + a2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-2.333333333a + a2 = -2.666666667

The a term is -2.333333333a.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333a + 1.361111112 + a2 = -2.666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333a + a2 = -2.666666667 + 1.361111112

Combine like terms: -2.666666667 + 1.361111112 = -1.305555555
1.361111112 + -2.333333333a + a2 = -1.305555555

Factor a perfect square on the left side:
(a + -1.166666667)(a + -1.166666667) = -1.305555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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