3a^2=3a-126

Solution for 3a^2=3a-126 equation:

Simplifying
3a2 = 3a + -126

Reorder the terms:
3a2 = -126 + 3a

Solving
3a2 = -126 + 3a

Solving for variable 'a'.

Reorder the terms:
126 + -3a + 3a2 = -126 + 3a + 126 + -3a

Reorder the terms:
126 + -3a + 3a2 = -126 + 126 + 3a + -3a

Combine like terms: -126 + 126 = 0
126 + -3a + 3a2 = 0 + 3a + -3a
126 + -3a + 3a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
126 + -3a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(42 + -1a + a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(42 + -1a + a2)' equal to zero and attempt to solve:

Simplifying
42 + -1a + a2 = 0

Solving
42 + -1a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -1a + -42 + a2 = 0 + -42

Reorder the terms:
42 + -42 + -1a + a2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1a + a2 = 0 + -42
-1a + a2 = 0 + -42

Combine like terms: 0 + -42 = -42
-1a + a2 = -42

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 = -42 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -42 + 0.25

Combine like terms: -42 + 0.25 = -41.75
0.25 + -1a + a2 = -41.75

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = -41.75

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.