15a^2+47a-26=-8a-6

Solution for 15a^2+47a-26=-8a-6 equation:

Simplifying
15a2 + 47a + -26 = -8a + -6

Reorder the terms:
-26 + 47a + 15a2 = -8a + -6

Reorder the terms:
-26 + 47a + 15a2 = -6 + -8a

Solving
-26 + 47a + 15a2 = -6 + -8a

Solving for variable 'a'.

Reorder the terms:
-26 + 6 + 47a + 8a + 15a2 = -6 + -8a + 6 + 8a

Combine like terms: -26 + 6 = -20
-20 + 47a + 8a + 15a2 = -6 + -8a + 6 + 8a

Combine like terms: 47a + 8a = 55a
-20 + 55a + 15a2 = -6 + -8a + 6 + 8a

Reorder the terms:
-20 + 55a + 15a2 = -6 + 6 + -8a + 8a

Combine like terms: -6 + 6 = 0
-20 + 55a + 15a2 = 0 + -8a + 8a
-20 + 55a + 15a2 = -8a + 8a

Combine like terms: -8a + 8a = 0
-20 + 55a + 15a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 11a + 3a2) = 0

Factor a trinomial.
5((-4 + -1a)(1 + -3a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 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 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(1 + -3a)' equal to zero and attempt to solve:

Simplifying
1 + -3a = 0

Solving
1 + -3a = 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 + -3a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3a = 0 + -1
-3a = 0 + -1

Combine like terms: 0 + -1 = -1
-3a = -1

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {-4, 0.3333333333}