x=2x^2-12x+18

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Solution for x=2x^2-12x+18 equation: 


Simplifying
x = 2x2 + -12x + 18

Reorder the terms:
x = 18 + -12x + 2x2

Solving
x = 18 + -12x + 2x2

Solving for variable 'x'.

Reorder the terms:
-18 + x + 12x + -2x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Combine like terms: x + 12x = 13x
-18 + 13x + -2x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Reorder the terms:
-18 + 13x + -2x2 = 18 + -18 + -12x + 12x + 2x2 + -2x2

Combine like terms: 18 + -18 = 0
-18 + 13x + -2x2 = 0 + -12x + 12x + 2x2 + -2x2
-18 + 13x + -2x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-18 + 13x + -2x2 = 0 + 2x2 + -2x2
-18 + 13x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18 + 13x + -2x2 = 0

Factor a trinomial.
(-9 + 2x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-9 + 2x)' equal to zero and attempt to solve:

Simplifying
-9 + 2x = 0

Solving
-9 + 2x = 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 + 2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x = 0 + 9
2x = 0 + 9

Combine like terms: 0 + 9 = 9
2x = 9

Divide each side by '2'.
x = 4.5

Simplifying
x = 4.5

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 = {4.5, 2}

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