8a^2-16a=6a-12

Solution for 8a^2-16a=6a-12 equation:

Simplifying
8a2 + -16a = 6a + -12

Reorder the terms:
-16a + 8a2 = 6a + -12

Reorder the terms:
-16a + 8a2 = -12 + 6a

Solving
-16a + 8a2 = -12 + 6a

Solving for variable 'a'.

Reorder the terms:
12 + -16a + -6a + 8a2 = -12 + 6a + 12 + -6a

Combine like terms: -16a + -6a = -22a
12 + -22a + 8a2 = -12 + 6a + 12 + -6a

Reorder the terms:
12 + -22a + 8a2 = -12 + 12 + 6a + -6a

Combine like terms: -12 + 12 = 0
12 + -22a + 8a2 = 0 + 6a + -6a
12 + -22a + 8a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
12 + -22a + 8a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -11a + 4a2) = 0

Factor a trinomial.
2((3 + -4a)(2 + -1a)) = 0

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

Simplifying
3 + -4a = 0

Solving
3 + -4a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a = 0 + -3
-4a = 0 + -3

Combine like terms: 0 + -3 = -3
-4a = -3

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
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 = {0.75, 2}