(x-5)(x-2)=28

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Solution for (x-5)(x-2)=28 equation: 


Simplifying
(x + -5)(x + -2) = 28

Reorder the terms:
(-5 + x)(x + -2) = 28

Reorder the terms:
(-5 + x)(-2 + x) = 28

Multiply (-5 + x) * (-2 + x)
(-5(-2 + x) + x(-2 + x)) = 28
((-2 * -5 + x * -5) + x(-2 + x)) = 28
((10 + -5x) + x(-2 + x)) = 28
(10 + -5x + (-2 * x + x * x)) = 28
(10 + -5x + (-2x + x2)) = 28

Combine like terms: -5x + -2x = -7x
(10 + -7x + x2) = 28

Solving
10 + -7x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
10 + -28 + -7x + x2 = 28 + -28

Combine like terms: 10 + -28 = -18
-18 + -7x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-18 + -7x + x2 = 0

Factor a trinomial.
(-2 + -1x)(9 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-2, 9}

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