-3a(a-2)+1=28

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Solution for -3a(a-2)+1=28 equation: 


Simplifying
-3a(a + -2) + 1 = 28

Reorder the terms:
-3a(-2 + a) + 1 = 28
(-2 * -3a + a * -3a) + 1 = 28
(6a + -3a2) + 1 = 28

Reorder the terms:
1 + 6a + -3a2 = 28

Solving
1 + 6a + -3a2 = 28

Solving for variable 'a'.

Reorder the terms:
1 + -28 + 6a + -3a2 = 28 + -28

Combine like terms: 1 + -28 = -27
-27 + 6a + -3a2 = 28 + -28

Combine like terms: 28 + -28 = 0
-27 + 6a + -3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 2a + -1a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + 2a + -1a2)' equal to zero and attempt to solve:

Simplifying
-9 + 2a + -1a2 = 0

Solving
-9 + 2a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
9 + -2a + a2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -2a + -9 + a2 = 0 + -9

Reorder the terms:
9 + -9 + -2a + a2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2a + a2 = 0 + -9
-2a + a2 = 0 + -9

Combine like terms: 0 + -9 = -9
-2a + a2 = -9

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = -9 + 1

Reorder the terms:
1 + -2a + a2 = -9 + 1

Combine like terms: -9 + 1 = -8
1 + -2a + a2 = -8

Factor a perfect square on the left side:
(a + -1)(a + -1) = -8

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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