(3x+1)(2x+5)=8

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Solution for (3x+1)(2x+5)=8 equation: 


Simplifying
(3x + 1)(2x + 5) = 8

Reorder the terms:
(1 + 3x)(2x + 5) = 8

Reorder the terms:
(1 + 3x)(5 + 2x) = 8

Multiply (1 + 3x) * (5 + 2x)
(1(5 + 2x) + 3x * (5 + 2x)) = 8
((5 * 1 + 2x * 1) + 3x * (5 + 2x)) = 8
((5 + 2x) + 3x * (5 + 2x)) = 8
(5 + 2x + (5 * 3x + 2x * 3x)) = 8
(5 + 2x + (15x + 6x2)) = 8

Combine like terms: 2x + 15x = 17x
(5 + 17x + 6x2) = 8

Solving
5 + 17x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
5 + -8 + 17x + 6x2 = 8 + -8

Combine like terms: 5 + -8 = -3
-3 + 17x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-3 + 17x + 6x2 = 0

Factor a trinomial.
(-3 + -1x)(1 + -6x) = 0


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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {-3, 0.1666666667}

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