32x=200+x^2+2x

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Solution for 32x=200+x^2+2x equation: 


Simplifying
32x = 200 + x2 + 2x

Reorder the terms:
32x = 200 + 2x + x2

Solving
32x = 200 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-200 + 32x + -2x + -1x2 = 200 + 2x + x2 + -200 + -2x + -1x2

Combine like terms: 32x + -2x = 30x
-200 + 30x + -1x2 = 200 + 2x + x2 + -200 + -2x + -1x2

Reorder the terms:
-200 + 30x + -1x2 = 200 + -200 + 2x + -2x + x2 + -1x2

Combine like terms: 200 + -200 = 0
-200 + 30x + -1x2 = 0 + 2x + -2x + x2 + -1x2
-200 + 30x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-200 + 30x + -1x2 = 0 + x2 + -1x2
-200 + 30x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-200 + 30x + -1x2 = 0

Factor a trinomial.
(-20 + x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-20 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 0

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

Add '20' to each side of the equation.
-20 + 20 + x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + x = 0 + 20
x = 0 + 20

Combine like terms: 0 + 20 = 20
x = 20

Simplifying
x = 20

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 = {20, 10}

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