2x=9x-18+8x^2

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Solution for 2x=9x-18+8x^2 equation: 


Simplifying
2x = 9x + -18 + 8x2

Reorder the terms:
2x = -18 + 9x + 8x2

Solving
2x = -18 + 9x + 8x2

Solving for variable 'x'.

Reorder the terms:
18 + 2x + -9x + -8x2 = -18 + 9x + 8x2 + 18 + -9x + -8x2

Combine like terms: 2x + -9x = -7x
18 + -7x + -8x2 = -18 + 9x + 8x2 + 18 + -9x + -8x2

Reorder the terms:
18 + -7x + -8x2 = -18 + 18 + 9x + -9x + 8x2 + -8x2

Combine like terms: -18 + 18 = 0
18 + -7x + -8x2 = 0 + 9x + -9x + 8x2 + -8x2
18 + -7x + -8x2 = 9x + -9x + 8x2 + -8x2

Combine like terms: 9x + -9x = 0
18 + -7x + -8x2 = 0 + 8x2 + -8x2
18 + -7x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
18 + -7x + -8x2 = 0

Factor a trinomial.
(9 + -8x)(2 + x) = 0


Subproblem 1
Set the factor '(9 + -8x)' equal to zero and attempt to solve:

Simplifying
9 + -8x = 0

Solving
9 + -8x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -8x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8x = 0 + -9
-8x = 0 + -9

Combine like terms: 0 + -9 = -9
-8x = -9

Divide each side by '-8'.
x = 1.125

Simplifying
x = 1.125

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {1.125, -2}

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