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

Factor a trinomial.
3((-6 + -1a)(7 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-6, 7}