(x-3)(x-5)=8

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Solution for (x-3)(x-5)=8 equation: 


Simplifying
(x + -3)(x + -5) = 8

Reorder the terms:
(-3 + x)(x + -5) = 8

Reorder the terms:
(-3 + x)(-5 + x) = 8

Multiply (-3 + x) * (-5 + x)
(-3(-5 + x) + x(-5 + x)) = 8
((-5 * -3 + x * -3) + x(-5 + x)) = 8
((15 + -3x) + x(-5 + x)) = 8
(15 + -3x + (-5 * x + x * x)) = 8
(15 + -3x + (-5x + x2)) = 8

Combine like terms: -3x + -5x = -8x
(15 + -8x + x2) = 8

Solving
15 + -8x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
15 + -8 + -8x + x2 = 8 + -8

Combine like terms: 15 + -8 = 7
7 + -8x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
7 + -8x + x2 = 0

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

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

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

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

Simplifying
x = 7
Solution
x = {1, 7}

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