(5a-4)(a+1)=a+16

Solution for (5a-4)(a+1)=a+16 equation:

Simplifying
(5a + -4)(a + 1) = a + 16

Reorder the terms:
(-4 + 5a)(a + 1) = a + 16

Reorder the terms:
(-4 + 5a)(1 + a) = a + 16

Multiply (-4 + 5a) * (1 + a)
(-4(1 + a) + 5a * (1 + a)) = a + 16
((1 * -4 + a * -4) + 5a * (1 + a)) = a + 16
((-4 + -4a) + 5a * (1 + a)) = a + 16
(-4 + -4a + (1 * 5a + a * 5a)) = a + 16
(-4 + -4a + (5a + 5a2)) = a + 16

Combine like terms: -4a + 5a = 1a
(-4 + 1a + 5a2) = a + 16

Reorder the terms:
-4 + 1a + 5a2 = 16 + a

Solving
-4 + 1a + 5a2 = 16 + a

Solving for variable 'a'.

Reorder the terms:
-4 + -16 + 1a + -1a + 5a2 = 16 + a + -16 + -1a

Combine like terms: -4 + -16 = -20
-20 + 1a + -1a + 5a2 = 16 + a + -16 + -1a

Combine like terms: 1a + -1a = 0
-20 + 0 + 5a2 = 16 + a + -16 + -1a
-20 + 5a2 = 16 + a + -16 + -1a

Reorder the terms:
-20 + 5a2 = 16 + -16 + a + -1a

Combine like terms: 16 + -16 = 0
-20 + 5a2 = 0 + a + -1a
-20 + 5a2 = a + -1a

Combine like terms: a + -1a = 0
-20 + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + a2) = 0

Factor a difference between two squares.
5((2 + a)(-2 + a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

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

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

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

Simplifying
-2 + a = 0

Solving
-2 + a = 0

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

Add '2' to each side of the equation.
-2 + 2 + a = 0 + 2

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

Combine like terms: 0 + 2 = 2
a = 2

Simplifying
a = 2
Solution
a = {-2, 2}