(x-7)(x+2)=22

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Solution for (x-7)(x+2)=22 equation: 


Simplifying
(x + -7)(x + 2) = 22

Reorder the terms:
(-7 + x)(x + 2) = 22

Reorder the terms:
(-7 + x)(2 + x) = 22

Multiply (-7 + x) * (2 + x)
(-7(2 + x) + x(2 + x)) = 22
((2 * -7 + x * -7) + x(2 + x)) = 22
((-14 + -7x) + x(2 + x)) = 22
(-14 + -7x + (2 * x + x * x)) = 22
(-14 + -7x + (2x + x2)) = 22

Combine like terms: -7x + 2x = -5x
(-14 + -5x + x2) = 22

Solving
-14 + -5x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
-14 + -22 + -5x + x2 = 22 + -22

Combine like terms: -14 + -22 = -36
-36 + -5x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-36 + -5x + x2 = 0

Factor a trinomial.
(-4 + -1x)(9 + -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 '(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 = {-4, 9}

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