(4a^2-1)=2a+1

Solution for (4a^2-1)=2a+1 equation:

Simplifying
(4a2 + -1) = 2a + 1

Reorder the terms:
(-1 + 4a2) = 2a + 1

Remove parenthesis around (-1 + 4a2)
-1 + 4a2 = 2a + 1

Reorder the terms:
-1 + 4a2 = 1 + 2a

Solving
-1 + 4a2 = 1 + 2a

Solving for variable 'a'.

Reorder the terms:
-1 + -1 + -2a + 4a2 = 1 + 2a + -1 + -2a

Combine like terms: -1 + -1 = -2
-2 + -2a + 4a2 = 1 + 2a + -1 + -2a

Reorder the terms:
-2 + -2a + 4a2 = 1 + -1 + 2a + -2a

Combine like terms: 1 + -1 = 0
-2 + -2a + 4a2 = 0 + 2a + -2a
-2 + -2a + 4a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
-2 + -2a + 4a2 = 0

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

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

Ignore the factor 2.
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 + -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 = {-0.5, 1}