4a+a(a+2)=40

Solution for 4a+a(a+2)=40 equation:

Simplifying
4a + a(a + 2) = 40

Reorder the terms:
4a + a(2 + a) = 40
4a + (2 * a + a * a) = 40
4a + (2a + a2) = 40

Combine like terms: 4a + 2a = 6a
6a + a2 = 40

Solving
6a + a2 = 40

Solving for variable 'a'.

Reorder the terms:
-40 + 6a + a2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 6a + a2 = 0

Factor a trinomial.
(-10 + -1a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-10 + -1a)' equal to zero and attempt to solve:

Simplifying
-10 + -1a = 0

Solving
-10 + -1a = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1a = 0 + 10
-1a = 0 + 10

Combine like terms: 0 + 10 = 10
-1a = 10

Divide each side by '-1'.
a = -10

Simplifying
a = -10
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 = {-10, 4}