(x-5)(x-7)=24

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Solution for (x-5)(x-7)=24 equation: 


Simplifying
(x + -5)(x + -7) = 24

Reorder the terms:
(-5 + x)(x + -7) = 24

Reorder the terms:
(-5 + x)(-7 + x) = 24

Multiply (-5 + x) * (-7 + x)
(-5(-7 + x) + x(-7 + x)) = 24
((-7 * -5 + x * -5) + x(-7 + x)) = 24
((35 + -5x) + x(-7 + x)) = 24
(35 + -5x + (-7 * x + x * x)) = 24
(35 + -5x + (-7x + x2)) = 24

Combine like terms: -5x + -7x = -12x
(35 + -12x + x2) = 24

Solving
35 + -12x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
35 + -24 + -12x + x2 = 24 + -24

Combine like terms: 35 + -24 = 11
11 + -12x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
11 + -12x + x2 = 0

Factor a trinomial.
(1 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {1, 11}

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