(x-5)(x-7)=0

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Solution for (x-5)(x-7)=0 equation: 


Simplifying
(x + -5)(x + -7) = 0

Reorder the terms:
(-5 + x)(x + -7) = 0

Reorder the terms:
(-5 + x)(-7 + x) = 0

Multiply (-5 + x) * (-7 + x)
(-5(-7 + x) + x(-7 + x)) = 0
((-7 * -5 + x * -5) + x(-7 + x)) = 0
((35 + -5x) + x(-7 + x)) = 0
(35 + -5x + (-7 * x + x * x)) = 0
(35 + -5x + (-7x + x2)) = 0

Combine like terms: -5x + -7x = -12x
(35 + -12x + x2) = 0

Solving
35 + -12x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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 = {5, 7}

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