(3x+2)(5x-22x+8)=0

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Solution for (3x+2)(5x-22x+8)=0 equation: 


Simplifying
(3x + 2)(5x + -22x + 8) = 0

Reorder the terms:
(2 + 3x)(5x + -22x + 8) = 0

Reorder the terms:
(2 + 3x)(8 + 5x + -22x) = 0

Combine like terms: 5x + -22x = -17x
(2 + 3x)(8 + -17x) = 0

Multiply (2 + 3x) * (8 + -17x)
(2(8 + -17x) + 3x * (8 + -17x)) = 0
((8 * 2 + -17x * 2) + 3x * (8 + -17x)) = 0
((16 + -34x) + 3x * (8 + -17x)) = 0
(16 + -34x + (8 * 3x + -17x * 3x)) = 0
(16 + -34x + (24x + -51x2)) = 0

Combine like terms: -34x + 24x = -10x
(16 + -10x + -51x2) = 0

Solving
16 + -10x + -51x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -17x)(2 + 3x) = 0


Subproblem 1
Set the factor '(8 + -17x)' equal to zero and attempt to solve:

Simplifying
8 + -17x = 0

Solving
8 + -17x = 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 + -17x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -17x = 0 + -8
-17x = 0 + -8

Combine like terms: 0 + -8 = -8
-17x = -8

Divide each side by '-17'.
x = 0.4705882353

Simplifying
x = 0.4705882353

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 = {0.4705882353, -0.6666666667}

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