19-3a(a-6)=66

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Solution for 19-3a(a-6)=66 equation: 


Simplifying
19 + -3a(a + -6) = 66

Reorder the terms:
19 + -3a(-6 + a) = 66
19 + (-6 * -3a + a * -3a) = 66
19 + (18a + -3a2) = 66

Solving
19 + 18a + -3a2 = 66

Solving for variable 'a'.

Reorder the terms:
19 + -66 + 18a + -3a2 = 66 + -66

Combine like terms: 19 + -66 = -47
-47 + 18a + -3a2 = 66 + -66

Combine like terms: 66 + -66 = 0
-47 + 18a + -3a2 = 0

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

Divide each side by '-3'.
15.66666667 + -6a + a2 = 0

Move the constant term to the right:

Add '-15.66666667' to each side of the equation.
15.66666667 + -6a + -15.66666667 + a2 = 0 + -15.66666667

Reorder the terms:
15.66666667 + -15.66666667 + -6a + a2 = 0 + -15.66666667

Combine like terms: 15.66666667 + -15.66666667 = 0.00000000
0.00000000 + -6a + a2 = 0 + -15.66666667
-6a + a2 = 0 + -15.66666667

Combine like terms: 0 + -15.66666667 = -15.66666667
-6a + a2 = -15.66666667

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = -15.66666667 + 9

Reorder the terms:
9 + -6a + a2 = -15.66666667 + 9

Combine like terms: -15.66666667 + 9 = -6.66666667
9 + -6a + a2 = -6.66666667

Factor a perfect square on the left side:
(a + -3)(a + -3) = -6.66666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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