(x-5)(x-2)=54

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Solution for (x-5)(x-2)=54 equation: 


Simplifying
(x + -5)(x + -2) = 54

Reorder the terms:
(-5 + x)(x + -2) = 54

Reorder the terms:
(-5 + x)(-2 + x) = 54

Multiply (-5 + x) * (-2 + x)
(-5(-2 + x) + x(-2 + x)) = 54
((-2 * -5 + x * -5) + x(-2 + x)) = 54
((10 + -5x) + x(-2 + x)) = 54
(10 + -5x + (-2 * x + x * x)) = 54
(10 + -5x + (-2x + x2)) = 54

Combine like terms: -5x + -2x = -7x
(10 + -7x + x2) = 54

Solving
10 + -7x + x2 = 54

Solving for variable 'x'.

Reorder the terms:
10 + -54 + -7x + x2 = 54 + -54

Combine like terms: 10 + -54 = -44
-44 + -7x + x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-44 + -7x + x2 = 0

Factor a trinomial.
(-4 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 11}

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