(x-3)(x-1)=24

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Solution for (x-3)(x-1)=24 equation: 


Simplifying
(x + -3)(x + -1) = 24

Reorder the terms:
(-3 + x)(x + -1) = 24

Reorder the terms:
(-3 + x)(-1 + x) = 24

Multiply (-3 + x) * (-1 + x)
(-3(-1 + x) + x(-1 + x)) = 24
((-1 * -3 + x * -3) + x(-1 + x)) = 24
((3 + -3x) + x(-1 + x)) = 24
(3 + -3x + (-1 * x + x * x)) = 24
(3 + -3x + (-1x + x2)) = 24

Combine like terms: -3x + -1x = -4x
(3 + -4x + x2) = 24

Solving
3 + -4x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
3 + -24 + -4x + x2 = 24 + -24

Combine like terms: 3 + -24 = -21
-21 + -4x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-21 + -4x + x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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 = {-3, 7}

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