x(5x+17)=2x^2-5x+16

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Solution for x(5x+17)=2x^2-5x+16 equation: 


Simplifying
x(5x + 17) = 2x2 + -5x + 16

Reorder the terms:
x(17 + 5x) = 2x2 + -5x + 16
(17 * x + 5x * x) = 2x2 + -5x + 16
(17x + 5x2) = 2x2 + -5x + 16

Reorder the terms:
17x + 5x2 = 16 + -5x + 2x2

Solving
17x + 5x2 = 16 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-16 + 17x + 5x + 5x2 + -2x2 = 16 + -5x + 2x2 + -16 + 5x + -2x2

Combine like terms: 17x + 5x = 22x
-16 + 22x + 5x2 + -2x2 = 16 + -5x + 2x2 + -16 + 5x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-16 + 22x + 3x2 = 16 + -5x + 2x2 + -16 + 5x + -2x2

Reorder the terms:
-16 + 22x + 3x2 = 16 + -16 + -5x + 5x + 2x2 + -2x2

Combine like terms: 16 + -16 = 0
-16 + 22x + 3x2 = 0 + -5x + 5x + 2x2 + -2x2
-16 + 22x + 3x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
-16 + 22x + 3x2 = 0 + 2x2 + -2x2
-16 + 22x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-16 + 22x + 3x2 = 0

Factor a trinomial.
(-8 + -1x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-8, 0.6666666667}

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