(x-1)(x+7)=9

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Solution for (x-1)(x+7)=9 equation: 


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

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

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

Multiply (-1 + x) * (7 + x)
(-1(7 + x) + x(7 + x)) = 9
((7 * -1 + x * -1) + x(7 + x)) = 9
((-7 + -1x) + x(7 + x)) = 9
(-7 + -1x + (7 * x + x * x)) = 9
(-7 + -1x + (7x + x2)) = 9

Combine like terms: -1x + 7x = 6x
(-7 + 6x + x2) = 9

Solving
-7 + 6x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-7 + -9 + 6x + x2 = 9 + -9

Combine like terms: -7 + -9 = -16
-16 + 6x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-16 + 6x + x2 = 0

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


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

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

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

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

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

Simplifying
x = -8

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

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

Simplifying
x = 2
Solution
x = {-8, 2}

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