x(5x+17)=2x^2-6x+36

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Solution for x(5x+17)=2x^2-6x+36 equation: 


Simplifying
x(5x + 17) = 2x2 + -6x + 36

Reorder the terms:
x(17 + 5x) = 2x2 + -6x + 36
(17 * x + 5x * x) = 2x2 + -6x + 36
(17x + 5x2) = 2x2 + -6x + 36

Reorder the terms:
17x + 5x2 = 36 + -6x + 2x2

Solving
17x + 5x2 = 36 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-36 + 17x + 6x + 5x2 + -2x2 = 36 + -6x + 2x2 + -36 + 6x + -2x2

Combine like terms: 17x + 6x = 23x
-36 + 23x + 5x2 + -2x2 = 36 + -6x + 2x2 + -36 + 6x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-36 + 23x + 3x2 = 36 + -6x + 2x2 + -36 + 6x + -2x2

Reorder the terms:
-36 + 23x + 3x2 = 36 + -36 + -6x + 6x + 2x2 + -2x2

Combine like terms: 36 + -36 = 0
-36 + 23x + 3x2 = 0 + -6x + 6x + 2x2 + -2x2
-36 + 23x + 3x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
-36 + 23x + 3x2 = 0 + 2x2 + -2x2
-36 + 23x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-36 + 23x + 3x2 = 0

Factor a trinomial.
(-9 + -1x)(4 + -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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-9, 1.333333333}

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