3a^2-10a=2a^2-16

Solution for 3a^2-10a=2a^2-16 equation:

Simplifying
3a2 + -10a = 2a2 + -16

Reorder the terms:
-10a + 3a2 = 2a2 + -16

Reorder the terms:
-10a + 3a2 = -16 + 2a2

Solving
-10a + 3a2 = -16 + 2a2

Solving for variable 'a'.

Reorder the terms:
16 + -10a + 3a2 + -2a2 = -16 + 2a2 + 16 + -2a2

Combine like terms: 3a2 + -2a2 = 1a2
16 + -10a + 1a2 = -16 + 2a2 + 16 + -2a2

Reorder the terms:
16 + -10a + 1a2 = -16 + 16 + 2a2 + -2a2

Combine like terms: -16 + 16 = 0
16 + -10a + 1a2 = 0 + 2a2 + -2a2
16 + -10a + 1a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
16 + -10a + 1a2 = 0

Factor a trinomial.
(2 + -1a)(8 + -1a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {2, 8}