(5a-4)(a+1)=a+41

Solution for (5a-4)(a+1)=a+41 equation:

Simplifying
(5a + -4)(a + 1) = a + 41

Reorder the terms:
(-4 + 5a)(a + 1) = a + 41

Reorder the terms:
(-4 + 5a)(1 + a) = a + 41

Multiply (-4 + 5a) * (1 + a)
(-4(1 + a) + 5a * (1 + a)) = a + 41
((1 * -4 + a * -4) + 5a * (1 + a)) = a + 41
((-4 + -4a) + 5a * (1 + a)) = a + 41
(-4 + -4a + (1 * 5a + a * 5a)) = a + 41
(-4 + -4a + (5a + 5a2)) = a + 41

Combine like terms: -4a + 5a = 1a
(-4 + 1a + 5a2) = a + 41

Reorder the terms:
-4 + 1a + 5a2 = 41 + a

Solving
-4 + 1a + 5a2 = 41 + a

Solving for variable 'a'.

Reorder the terms:
-4 + -41 + 1a + -1a + 5a2 = 41 + a + -41 + -1a

Combine like terms: -4 + -41 = -45
-45 + 1a + -1a + 5a2 = 41 + a + -41 + -1a

Combine like terms: 1a + -1a = 0
-45 + 0 + 5a2 = 41 + a + -41 + -1a
-45 + 5a2 = 41 + a + -41 + -1a

Reorder the terms:
-45 + 5a2 = 41 + -41 + a + -1a

Combine like terms: 41 + -41 = 0
-45 + 5a2 = 0 + a + -1a
-45 + 5a2 = a + -1a

Combine like terms: a + -1a = 0
-45 + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + a2) = 0

Factor a difference between two squares.
5((3 + a)(-3 + a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(-3 + a)' equal to zero and attempt to solve:

Simplifying
-3 + a = 0

Solving
-3 + a = 0

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

Add '3' to each side of the equation.
-3 + 3 + a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + a = 0 + 3
a = 0 + 3

Combine like terms: 0 + 3 = 3
a = 3

Simplifying
a = 3
Solution
a = {-3, 3}