x^2-7x+x+20=180

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Solution for x^2-7x+x+20=180 equation: 


Simplifying
x2 + -7x + x + 20 = 180

Reorder the terms:
20 + -7x + x + x2 = 180

Combine like terms: -7x + x = -6x
20 + -6x + x2 = 180

Solving
20 + -6x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
20 + -180 + -6x + x2 = 180 + -180

Combine like terms: 20 + -180 = -160
-160 + -6x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-160 + -6x + x2 = 0

Factor a trinomial.
(-10 + -1x)(16 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-10, 16}

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