x(5x+23)=2x^2-3x+9

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 23x + 3x = 26x
-9 + 26x + 5x2 + -2x2 = 9 + -3x + 2x2 + -9 + 3x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-9 + 26x + 3x2 = 9 + -3x + 2x2 + -9 + 3x + -2x2

Reorder the terms:
-9 + 26x + 3x2 = 9 + -9 + -3x + 3x + 2x2 + -2x2

Combine like terms: 9 + -9 = 0
-9 + 26x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2
-9 + 26x + 3x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-9 + 26x + 3x2 = 0 + 2x2 + -2x2
-9 + 26x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-9 + 26x + 3x2 = 0

Factor a trinomial.
(-9 + -1x)(1 + -3x) = 0


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

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 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 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-9, 0.3333333333}

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