(x-2)(x-7)=36

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Solution for (x-2)(x-7)=36 equation: 


Simplifying
(x + -2)(x + -7) = 36

Reorder the terms:
(-2 + x)(x + -7) = 36

Reorder the terms:
(-2 + x)(-7 + x) = 36

Multiply (-2 + x) * (-7 + x)
(-2(-7 + x) + x(-7 + x)) = 36
((-7 * -2 + x * -2) + x(-7 + x)) = 36
((14 + -2x) + x(-7 + x)) = 36
(14 + -2x + (-7 * x + x * x)) = 36
(14 + -2x + (-7x + x2)) = 36

Combine like terms: -2x + -7x = -9x
(14 + -9x + x2) = 36

Solving
14 + -9x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
14 + -36 + -9x + x2 = 36 + -36

Combine like terms: 14 + -36 = -22
-22 + -9x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-22 + -9x + x2 = 0

Factor a trinomial.
(-2 + -1x)(11 + -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 '(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 = {-2, 11}

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