42+9x=x^2+3x+2

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Solution for 42+9x=x^2+3x+2 equation: 


Simplifying
42 + 9x = x2 + 3x + 2

Reorder the terms:
42 + 9x = 2 + 3x + x2

Solving
42 + 9x = 2 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
42 + -2 + 9x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 42 + -2 = 40
40 + 9x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 9x + -3x = 6x
40 + 6x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Reorder the terms:
40 + 6x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
40 + 6x + -1x2 = 0 + 3x + -3x + x2 + -1x2
40 + 6x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
40 + 6x + -1x2 = 0 + x2 + -1x2
40 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
40 + 6x + -1x2 = 0

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

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

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