12a^2-4a-13=5a+8

Solution for 12a^2-4a-13=5a+8 equation:

Simplifying
12a2 + -4a + -13 = 5a + 8

Reorder the terms:
-13 + -4a + 12a2 = 5a + 8

Reorder the terms:
-13 + -4a + 12a2 = 8 + 5a

Solving
-13 + -4a + 12a2 = 8 + 5a

Solving for variable 'a'.

Reorder the terms:
-13 + -8 + -4a + -5a + 12a2 = 8 + 5a + -8 + -5a

Combine like terms: -13 + -8 = -21
-21 + -4a + -5a + 12a2 = 8 + 5a + -8 + -5a

Combine like terms: -4a + -5a = -9a
-21 + -9a + 12a2 = 8 + 5a + -8 + -5a

Reorder the terms:
-21 + -9a + 12a2 = 8 + -8 + 5a + -5a

Combine like terms: 8 + -8 = 0
-21 + -9a + 12a2 = 0 + 5a + -5a
-21 + -9a + 12a2 = 5a + -5a

Combine like terms: 5a + -5a = 0
-21 + -9a + 12a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -3a + 4a2) = 0

Factor a trinomial.
3((-1 + -1a)(7 + -4a)) = 0

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
Subproblem 2
Set the factor '(7 + -4a)' equal to zero and attempt to solve:

Simplifying
7 + -4a = 0

Solving
7 + -4a = 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 + -4a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4a = 0 + -7
-4a = 0 + -7

Combine like terms: 0 + -7 = -7
-4a = -7

Divide each side by '-4'.
a = 1.75

Simplifying
a = 1.75
Solution
a = {-1, 1.75}