15a^2-8=29a+6

Solution for 15a^2-8=29a+6 equation:

Simplifying
15a2 + -8 = 29a + 6

Reorder the terms:
-8 + 15a2 = 29a + 6

Reorder the terms:
-8 + 15a2 = 6 + 29a

Solving
-8 + 15a2 = 6 + 29a

Solving for variable 'a'.

Reorder the terms:
-8 + -6 + -29a + 15a2 = 6 + 29a + -6 + -29a

Combine like terms: -8 + -6 = -14
-14 + -29a + 15a2 = 6 + 29a + -6 + -29a

Reorder the terms:
-14 + -29a + 15a2 = 6 + -6 + 29a + -29a

Combine like terms: 6 + -6 = 0
-14 + -29a + 15a2 = 0 + 29a + -29a
-14 + -29a + 15a2 = 29a + -29a

Combine like terms: 29a + -29a = 0
-14 + -29a + 15a2 = 0

Factor a trinomial.
(-2 + -5a)(7 + -3a) = 0

Subproblem 1
Set the factor '(-2 + -5a)' equal to zero and attempt to solve:

Simplifying
-2 + -5a = 0

Solving
-2 + -5a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5a = 0 + 2
-5a = 0 + 2

Combine like terms: 0 + 2 = 2
-5a = 2

Divide each side by '-5'.
a = -0.4

Simplifying
a = -0.4
Subproblem 2
Set the factor '(7 + -3a)' equal to zero and attempt to solve:

Simplifying
7 + -3a = 0

Solving
7 + -3a = 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 + -3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3a = 0 + -7
-3a = 0 + -7

Combine like terms: 0 + -7 = -7
-3a = -7

Divide each side by '-3'.
a = 2.333333333

Simplifying
a = 2.333333333
Solution
a = {-0.4, 2.333333333}