(x-3)(x+6)=9x+22

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Solution for (x-3)(x+6)=9x+22 equation: 


Simplifying
(x + -3)(x + 6) = 9x + 22

Reorder the terms:
(-3 + x)(x + 6) = 9x + 22

Reorder the terms:
(-3 + x)(6 + x) = 9x + 22

Multiply (-3 + x) * (6 + x)
(-3(6 + x) + x(6 + x)) = 9x + 22
((6 * -3 + x * -3) + x(6 + x)) = 9x + 22
((-18 + -3x) + x(6 + x)) = 9x + 22
(-18 + -3x + (6 * x + x * x)) = 9x + 22
(-18 + -3x + (6x + x2)) = 9x + 22

Combine like terms: -3x + 6x = 3x
(-18 + 3x + x2) = 9x + 22

Reorder the terms:
-18 + 3x + x2 = 22 + 9x

Solving
-18 + 3x + x2 = 22 + 9x

Solving for variable 'x'.

Reorder the terms:
-18 + -22 + 3x + -9x + x2 = 22 + 9x + -22 + -9x

Combine like terms: -18 + -22 = -40
-40 + 3x + -9x + x2 = 22 + 9x + -22 + -9x

Combine like terms: 3x + -9x = -6x
-40 + -6x + x2 = 22 + 9x + -22 + -9x

Reorder the terms:
-40 + -6x + x2 = 22 + -22 + 9x + -9x

Combine like terms: 22 + -22 = 0
-40 + -6x + x2 = 0 + 9x + -9x
-40 + -6x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-40 + -6x + x2 = 0

Factor a trinomial.
(-4 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-4, 10}

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