3x^2-23x=-2x^2-5x-9

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Solution for 3x^2-23x=-2x^2-5x-9 equation: 


Simplifying
3x2 + -23x = -2x2 + -5x + -9

Reorder the terms:
-23x + 3x2 = -2x2 + -5x + -9

Reorder the terms:
-23x + 3x2 = -9 + -5x + -2x2

Solving
-23x + 3x2 = -9 + -5x + -2x2

Solving for variable 'x'.

Reorder the terms:
9 + -23x + 5x + 3x2 + 2x2 = -9 + -5x + -2x2 + 9 + 5x + 2x2

Combine like terms: -23x + 5x = -18x
9 + -18x + 3x2 + 2x2 = -9 + -5x + -2x2 + 9 + 5x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
9 + -18x + 5x2 = -9 + -5x + -2x2 + 9 + 5x + 2x2

Reorder the terms:
9 + -18x + 5x2 = -9 + 9 + -5x + 5x + -2x2 + 2x2

Combine like terms: -9 + 9 = 0
9 + -18x + 5x2 = 0 + -5x + 5x + -2x2 + 2x2
9 + -18x + 5x2 = -5x + 5x + -2x2 + 2x2

Combine like terms: -5x + 5x = 0
9 + -18x + 5x2 = 0 + -2x2 + 2x2
9 + -18x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
9 + -18x + 5x2 = 0

Factor a trinomial.
(3 + -5x)(3 + -1x) = 0


Subproblem 1
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.6, 3}

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