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

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

Simplifying
2a(a + 4) + -1(a + 4) = 0

Reorder the terms:
2a(4 + a) + -1(a + 4) = 0
(4 * 2a + a * 2a) + -1(a + 4) = 0
(8a + 2a2) + -1(a + 4) = 0

Reorder the terms:
8a + 2a2 + -1(4 + a) = 0
8a + 2a2 + (4 * -1 + a * -1) = 0
8a + 2a2 + (-4 + -1a) = 0

Reorder the terms:
-4 + 8a + -1a + 2a2 = 0

Combine like terms: 8a + -1a = 7a
-4 + 7a + 2a2 = 0

Solving
-4 + 7a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-4 + -1a)(1 + -2a) = 0

Subproblem 1
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
Subproblem 2
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
Solution
a = {-4, 0.5}