(5a+1)(a-1)=3(1-a)

Solution for (5a+1)(a-1)=3(1-a) equation:

Simplifying
(5a + 1)(a + -1) = 3(1 + -1a)

Reorder the terms:
(1 + 5a)(a + -1) = 3(1 + -1a)

Reorder the terms:
(1 + 5a)(-1 + a) = 3(1 + -1a)

Multiply (1 + 5a) * (-1 + a)
(1(-1 + a) + 5a * (-1 + a)) = 3(1 + -1a)
((-1 * 1 + a * 1) + 5a * (-1 + a)) = 3(1 + -1a)
((-1 + 1a) + 5a * (-1 + a)) = 3(1 + -1a)
(-1 + 1a + (-1 * 5a + a * 5a)) = 3(1 + -1a)
(-1 + 1a + (-5a + 5a2)) = 3(1 + -1a)

Combine like terms: 1a + -5a = -4a
(-1 + -4a + 5a2) = 3(1 + -1a)
-1 + -4a + 5a2 = (1 * 3 + -1a * 3)
-1 + -4a + 5a2 = (3 + -3a)

Solving
-1 + -4a + 5a2 = 3 + -3a

Solving for variable 'a'.

Reorder the terms:
-1 + -3 + -4a + 3a + 5a2 = 3 + -3a + -3 + 3a

Combine like terms: -1 + -3 = -4
-4 + -4a + 3a + 5a2 = 3 + -3a + -3 + 3a

Combine like terms: -4a + 3a = -1a
-4 + -1a + 5a2 = 3 + -3a + -3 + 3a

Reorder the terms:
-4 + -1a + 5a2 = 3 + -3 + -3a + 3a

Combine like terms: 3 + -3 = 0
-4 + -1a + 5a2 = 0 + -3a + 3a
-4 + -1a + 5a2 = -3a + 3a

Combine like terms: -3a + 3a = 0
-4 + -1a + 5a2 = 0

Factor a trinomial.
(-4 + -5a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-4 + -5a)' equal to zero and attempt to solve:

Simplifying
-4 + -5a = 0

Solving
-4 + -5a = 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 + -5a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5a = 0 + 4
-5a = 0 + 4

Combine like terms: 0 + 4 = 4
-5a = 4

Divide each side by '-5'.
a = -0.8

Simplifying
a = -0.8
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 = {-0.8, 1}