(2x^2+9x+4)-(x^2+3x+2)-18=0

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Solution for (2x^2+9x+4)-(x^2+3x+2)-18=0 equation: 


Simplifying
(2x2 + 9x + 4) + -1(x2 + 3x + 2) + -18 = 0

Reorder the terms:
(4 + 9x + 2x2) + -1(x2 + 3x + 2) + -18 = 0

Remove parenthesis around (4 + 9x + 2x2)
4 + 9x + 2x2 + -1(x2 + 3x + 2) + -18 = 0

Reorder the terms:
4 + 9x + 2x2 + -1(2 + 3x + x2) + -18 = 0
4 + 9x + 2x2 + (2 * -1 + 3x * -1 + x2 * -1) + -18 = 0
4 + 9x + 2x2 + (-2 + -3x + -1x2) + -18 = 0

Reorder the terms:
4 + -2 + -18 + 9x + -3x + 2x2 + -1x2 = 0

Combine like terms: 4 + -2 = 2
2 + -18 + 9x + -3x + 2x2 + -1x2 = 0

Combine like terms: 2 + -18 = -16
-16 + 9x + -3x + 2x2 + -1x2 = 0

Combine like terms: 9x + -3x = 6x
-16 + 6x + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
-16 + 6x + 1x2 = 0

Solving
-16 + 6x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-8, 2}

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