13a^2-46a-32=6a^2+6a

Solution for 13a^2-46a-32=6a^2+6a equation:

Simplifying
13a2 + -46a + -32 = 6a2 + 6a

Reorder the terms:
-32 + -46a + 13a2 = 6a2 + 6a

Reorder the terms:
-32 + -46a + 13a2 = 6a + 6a2

Solving
-32 + -46a + 13a2 = 6a + 6a2

Solving for variable 'a'.

Reorder the terms:
-32 + -46a + -6a + 13a2 + -6a2 = 6a + 6a2 + -6a + -6a2

Combine like terms: -46a + -6a = -52a
-32 + -52a + 13a2 + -6a2 = 6a + 6a2 + -6a + -6a2

Combine like terms: 13a2 + -6a2 = 7a2
-32 + -52a + 7a2 = 6a + 6a2 + -6a + -6a2

Reorder the terms:
-32 + -52a + 7a2 = 6a + -6a + 6a2 + -6a2

Combine like terms: 6a + -6a = 0
-32 + -52a + 7a2 = 0 + 6a2 + -6a2
-32 + -52a + 7a2 = 6a2 + -6a2

Combine like terms: 6a2 + -6a2 = 0
-32 + -52a + 7a2 = 0

Factor a trinomial.
(-4 + -7a)(8 + -1a) = 0

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

Simplifying
-4 + -7a = 0

Solving
-4 + -7a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7a = 0 + 4

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

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

Divide each side by '-7'.
a = -0.5714285714

Simplifying
a = -0.5714285714
Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {-0.5714285714, 8}