(x-6)(x+3)=22

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Solution for (x-6)(x+3)=22 equation: 


Simplifying
(x + -6)(x + 3) = 22

Reorder the terms:
(-6 + x)(x + 3) = 22

Reorder the terms:
(-6 + x)(3 + x) = 22

Multiply (-6 + x) * (3 + x)
(-6(3 + x) + x(3 + x)) = 22
((3 * -6 + x * -6) + x(3 + x)) = 22
((-18 + -6x) + x(3 + x)) = 22
(-18 + -6x + (3 * x + x * x)) = 22
(-18 + -6x + (3x + x2)) = 22

Combine like terms: -6x + 3x = -3x
(-18 + -3x + x2) = 22

Solving
-18 + -3x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
-18 + -22 + -3x + x2 = 22 + -22

Combine like terms: -18 + -22 = -40
-40 + -3x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-40 + -3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-5, 8}

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