(x-3)(x-9)=7

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Solution for (x-3)(x-9)=7 equation: 


Simplifying
(x + -3)(x + -9) = 7

Reorder the terms:
(-3 + x)(x + -9) = 7

Reorder the terms:
(-3 + x)(-9 + x) = 7

Multiply (-3 + x) * (-9 + x)
(-3(-9 + x) + x(-9 + x)) = 7
((-9 * -3 + x * -3) + x(-9 + x)) = 7
((27 + -3x) + x(-9 + x)) = 7
(27 + -3x + (-9 * x + x * x)) = 7
(27 + -3x + (-9x + x2)) = 7

Combine like terms: -3x + -9x = -12x
(27 + -12x + x2) = 7

Solving
27 + -12x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
27 + -7 + -12x + x2 = 7 + -7

Combine like terms: 27 + -7 = 20
20 + -12x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
20 + -12x + x2 = 0

Factor a trinomial.
(2 + -1x)(10 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {2, 10}

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