(a-9)(a-1)=-7

Solution for (a-9)(a-1)=-7 equation:

Simplifying
(a + -9)(a + -1) = -7

Reorder the terms:
(-9 + a)(a + -1) = -7

Reorder the terms:
(-9 + a)(-1 + a) = -7

Multiply (-9 + a) * (-1 + a)
(-9(-1 + a) + a(-1 + a)) = -7
((-1 * -9 + a * -9) + a(-1 + a)) = -7
((9 + -9a) + a(-1 + a)) = -7
(9 + -9a + (-1 * a + a * a)) = -7
(9 + -9a + (-1a + a2)) = -7

Combine like terms: -9a + -1a = -10a
(9 + -10a + a2) = -7

Solving
9 + -10a + a2 = -7

Solving for variable 'a'.

Reorder the terms:
9 + 7 + -10a + a2 = -7 + 7

Combine like terms: 9 + 7 = 16
16 + -10a + a2 = -7 + 7

Combine like terms: -7 + 7 = 0
16 + -10a + a2 = 0

Factor a trinomial.
(2 + -1a)(8 + -1a) = 0

Subproblem 1
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {2, 8}