35=a(a+2)

Solution for 35=a(a+2) equation:

Simplifying
35 = a(a + 2)

Reorder the terms:
35 = a(2 + a)
35 = (2 * a + a * a)
35 = (2a + a2)

Solving
35 = 2a + a2

Solving for variable 'a'.

Reorder the terms:
35 + -2a + -1a2 = 2a + -2a + a2 + -1a2

Combine like terms: 2a + -2a = 0
35 + -2a + -1a2 = 0 + a2 + -1a2
35 + -2a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
35 + -2a + -1a2 = 0

Factor a trinomial.
(5 + -1a)(7 + a) = 0

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

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

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

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

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 0

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

Add '-7' to each side of the equation.
7 + -7 + a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + a = 0 + -7
a = 0 + -7

Combine like terms: 0 + -7 = -7
a = -7

Simplifying
a = -7
Solution
a = {5, -7}