(3x+2)(x+5)=170

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Solution for (3x+2)(x+5)=170 equation: 


Simplifying
(3x + 2)(x + 5) = 170

Reorder the terms:
(2 + 3x)(x + 5) = 170

Reorder the terms:
(2 + 3x)(5 + x) = 170

Multiply (2 + 3x) * (5 + x)
(2(5 + x) + 3x * (5 + x)) = 170
((5 * 2 + x * 2) + 3x * (5 + x)) = 170
((10 + 2x) + 3x * (5 + x)) = 170
(10 + 2x + (5 * 3x + x * 3x)) = 170
(10 + 2x + (15x + 3x2)) = 170

Combine like terms: 2x + 15x = 17x
(10 + 17x + 3x2) = 170

Solving
10 + 17x + 3x2 = 170

Solving for variable 'x'.

Reorder the terms:
10 + -170 + 17x + 3x2 = 170 + -170

Combine like terms: 10 + -170 = -160
-160 + 17x + 3x2 = 170 + -170

Combine like terms: 170 + -170 = 0
-160 + 17x + 3x2 = 0

Factor a trinomial.
(-32 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-32 + -3x)' equal to zero and attempt to solve:

Simplifying
-32 + -3x = 0

Solving
-32 + -3x = 0

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

Add '32' to each side of the equation.
-32 + 32 + -3x = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -3x = 0 + 32
-3x = 0 + 32

Combine like terms: 0 + 32 = 32
-3x = 32

Divide each side by '-3'.
x = -10.66666667

Simplifying
x = -10.66666667

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-10.66666667, 5}

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