4a^2-4a-5=-6

Solution for 4a^2-4a-5=-6 equation:

Simplifying
4a2 + -4a + -5 = -6

Reorder the terms:
-5 + -4a + 4a2 = -6

Solving
-5 + -4a + 4a2 = -6

Solving for variable 'a'.

Reorder the terms:
-5 + 6 + -4a + 4a2 = -6 + 6

Combine like terms: -5 + 6 = 1
1 + -4a + 4a2 = -6 + 6

Combine like terms: -6 + 6 = 0
1 + -4a + 4a2 = 0

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

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 '(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
Solution
a = {0.5, 0.5}