a(a-7)+9(a-7)=

Solution for a(a-7)+9(a-7)= equation:

Simplifying
a(a + -7) + 9(a + -7) = 0

Reorder the terms:
a(-7 + a) + 9(a + -7) = 0
(-7 * a + a * a) + 9(a + -7) = 0
(-7a + a2) + 9(a + -7) = 0

Reorder the terms:
-7a + a2 + 9(-7 + a) = 0
-7a + a2 + (-7 * 9 + a * 9) = 0
-7a + a2 + (-63 + 9a) = 0

Reorder the terms:
-63 + -7a + 9a + a2 = 0

Combine like terms: -7a + 9a = 2a
-63 + 2a + a2 = 0

Solving
-63 + 2a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-9 + -1a)(7 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
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 = {-9, 7}