2(3a^2-5)=8a+4

Solution for 2(3a^2-5)=8a+4 equation:

Simplifying
2(3a2 + -5) = 8a + 4

Reorder the terms:
2(-5 + 3a2) = 8a + 4
(-5 * 2 + 3a2 * 2) = 8a + 4
(-10 + 6a2) = 8a + 4

Reorder the terms:
-10 + 6a2 = 4 + 8a

Solving
-10 + 6a2 = 4 + 8a

Solving for variable 'a'.

Reorder the terms:
-10 + -4 + -8a + 6a2 = 4 + 8a + -4 + -8a

Combine like terms: -10 + -4 = -14
-14 + -8a + 6a2 = 4 + 8a + -4 + -8a

Reorder the terms:
-14 + -8a + 6a2 = 4 + -4 + 8a + -8a

Combine like terms: 4 + -4 = 0
-14 + -8a + 6a2 = 0 + 8a + -8a
-14 + -8a + 6a2 = 8a + -8a

Combine like terms: 8a + -8a = 0
-14 + -8a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -4a + 3a2) = 0

Factor a trinomial.
2((-1 + -1a)(7 + -3a)) = 0

Ignore the factor 2.
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 + -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 = {-1, 2.333333333}