2x+10=42-2x-x^2

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Solution for 2x+10=42-2x-x^2 equation: 


Simplifying
2x + 10 = 42 + -2x + -1x2

Reorder the terms:
10 + 2x = 42 + -2x + -1x2

Solving
10 + 2x = 42 + -2x + -1x2

Solving for variable 'x'.

Reorder the terms:
10 + -42 + 2x + 2x + x2 = 42 + -2x + -1x2 + -42 + 2x + x2

Combine like terms: 10 + -42 = -32
-32 + 2x + 2x + x2 = 42 + -2x + -1x2 + -42 + 2x + x2

Combine like terms: 2x + 2x = 4x
-32 + 4x + x2 = 42 + -2x + -1x2 + -42 + 2x + x2

Reorder the terms:
-32 + 4x + x2 = 42 + -42 + -2x + 2x + -1x2 + x2

Combine like terms: 42 + -42 = 0
-32 + 4x + x2 = 0 + -2x + 2x + -1x2 + x2
-32 + 4x + x2 = -2x + 2x + -1x2 + x2

Combine like terms: -2x + 2x = 0
-32 + 4x + x2 = 0 + -1x2 + x2
-32 + 4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-32 + 4x + x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-8, 4}

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