3a(2a)=6a-6

Solution for 3a(2a)=6a-6 equation:

Simplifying
3a(2a) = 6a + -6

Remove parenthesis around (2a)
3a * 2a = 6a + -6

Reorder the terms for easier multiplication:
3 * 2a * a = 6a + -6

Multiply 3 * 2
6a * a = 6a + -6

Multiply a * a
6a2 = 6a + -6

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

Solving
6a2 = -6 + 6a

Solving for variable 'a'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + -1a + a2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -1a + a2)' equal to zero and attempt to solve:

Simplifying
1 + -1a + a2 = 0

Solving
1 + -1a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + -1a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a + a2 = 0 + -1
-1a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1a + a2 = -1

The a term is -1a.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = -1 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + -1a + a2 = -0.75

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = -0.75

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.