2a^2=-6a+8a

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

Simplifying
2a2 = -6a + 8a

Combine like terms: -6a + 8a = 2a
2a2 = 2a

Solving
2a2 = 2a

Solving for variable 'a'.

Reorder the terms:
-2a + 2a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
-2a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(-1 + a) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-1 + a)' equal to zero and attempt to solve:

Simplifying
-1 + a = 0

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

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

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

Simplifying
a = 1
Solution
a = {0, 1}