(4a-6)2a=8

Solution for (4a-6)2a=8 equation:

Simplifying
(4a + -6) * 2a = 8

Reorder the terms:
(-6 + 4a) * 2a = 8

Reorder the terms for easier multiplication:
2a(-6 + 4a) = 8
(-6 * 2a + 4a * 2a) = 8
(-12a + 8a2) = 8

Solving
-12a + 8a2 = 8

Solving for variable 'a'.

Reorder the terms:
-8 + -12a + 8a2 = 8 + -8

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

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

Factor a trinomial.
4((-1 + -2a)(2 + -1a)) = 0

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-0.5, 2}