4x^2-23x+45=2x+9

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Solution for 4x^2-23x+45=2x+9 equation: 


Simplifying
4x2 + -23x + 45 = 2x + 9

Reorder the terms:
45 + -23x + 4x2 = 2x + 9

Reorder the terms:
45 + -23x + 4x2 = 9 + 2x

Solving
45 + -23x + 4x2 = 9 + 2x

Solving for variable 'x'.

Reorder the terms:
45 + -9 + -23x + -2x + 4x2 = 9 + 2x + -9 + -2x

Combine like terms: 45 + -9 = 36
36 + -23x + -2x + 4x2 = 9 + 2x + -9 + -2x

Combine like terms: -23x + -2x = -25x
36 + -25x + 4x2 = 9 + 2x + -9 + -2x

Reorder the terms:
36 + -25x + 4x2 = 9 + -9 + 2x + -2x

Combine like terms: 9 + -9 = 0
36 + -25x + 4x2 = 0 + 2x + -2x
36 + -25x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
36 + -25x + 4x2 = 0

Factor a trinomial.
(9 + -4x)(4 + -1x) = 0


Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2.25, 4}

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