2x^2-6x+9=7x-9

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Solution for 2x^2-6x+9=7x-9 equation: 


Simplifying
2x2 + -6x + 9 = 7x + -9

Reorder the terms:
9 + -6x + 2x2 = 7x + -9

Reorder the terms:
9 + -6x + 2x2 = -9 + 7x

Solving
9 + -6x + 2x2 = -9 + 7x

Solving for variable 'x'.

Reorder the terms:
9 + 9 + -6x + -7x + 2x2 = -9 + 7x + 9 + -7x

Combine like terms: 9 + 9 = 18
18 + -6x + -7x + 2x2 = -9 + 7x + 9 + -7x

Combine like terms: -6x + -7x = -13x
18 + -13x + 2x2 = -9 + 7x + 9 + -7x

Reorder the terms:
18 + -13x + 2x2 = -9 + 9 + 7x + -7x

Combine like terms: -9 + 9 = 0
18 + -13x + 2x2 = 0 + 7x + -7x
18 + -13x + 2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
18 + -13x + 2x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {2, 4.5}

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