4x^2-9x+9=2x+3

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Solution for 4x^2-9x+9=2x+3 equation: 


Simplifying
4x2 + -9x + 9 = 2x + 3

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

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

Solving
9 + -9x + 4x2 = 3 + 2x

Solving for variable 'x'.

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

Combine like terms: 9 + -3 = 6
6 + -9x + -2x + 4x2 = 3 + 2x + -3 + -2x

Combine like terms: -9x + -2x = -11x
6 + -11x + 4x2 = 3 + 2x + -3 + -2x

Reorder the terms:
6 + -11x + 4x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
6 + -11x + 4x2 = 0 + 2x + -2x
6 + -11x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + -11x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

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 = {0.75, 2}

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