(2a-1)(a+1)=8a+3

Solution for (2a-1)(a+1)=8a+3 equation:

Simplifying
(2a + -1)(a + 1) = 8a + 3

Reorder the terms:
(-1 + 2a)(a + 1) = 8a + 3

Reorder the terms:
(-1 + 2a)(1 + a) = 8a + 3

Multiply (-1 + 2a) * (1 + a)
(-1(1 + a) + 2a * (1 + a)) = 8a + 3
((1 * -1 + a * -1) + 2a * (1 + a)) = 8a + 3
((-1 + -1a) + 2a * (1 + a)) = 8a + 3
(-1 + -1a + (1 * 2a + a * 2a)) = 8a + 3
(-1 + -1a + (2a + 2a2)) = 8a + 3

Combine like terms: -1a + 2a = 1a
(-1 + 1a + 2a2) = 8a + 3

Reorder the terms:
-1 + 1a + 2a2 = 3 + 8a

Solving
-1 + 1a + 2a2 = 3 + 8a

Solving for variable 'a'.

Reorder the terms:
-1 + -3 + 1a + -8a + 2a2 = 3 + 8a + -3 + -8a

Combine like terms: -1 + -3 = -4
-4 + 1a + -8a + 2a2 = 3 + 8a + -3 + -8a

Combine like terms: 1a + -8a = -7a
-4 + -7a + 2a2 = 3 + 8a + -3 + -8a

Reorder the terms:
-4 + -7a + 2a2 = 3 + -3 + 8a + -8a

Combine like terms: 3 + -3 = 0
-4 + -7a + 2a2 = 0 + 8a + -8a
-4 + -7a + 2a2 = 8a + -8a

Combine like terms: 8a + -8a = 0
-4 + -7a + 2a2 = 0

Factor a trinomial.
(-1 + -2a)(4 + -1a) = 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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

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

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

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-0.5, 4}