a(a-2)=35

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

Simplifying
a(a + -2) = 35

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

Solving
-2a + a2 = 35

Solving for variable 'a'.

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

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

Factor a trinomial.
(-5 + -1a)(7 + -1a) = 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 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 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 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

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