4a^2=8a-4

Solution for 4a^2=8a-4 equation:

Simplifying
4a2 = 8a + -4

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

Solving
4a2 = -4 + 8a

Solving for variable 'a'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -2a + a2) = 0

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

Ignore the factor 4.
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 '(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
Solution
a = {1, 1}