(3x+6)(6x+5)=0

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Solution for (3x+6)(6x+5)=0 equation: 


Simplifying
(3x + 6)(6x + 5) = 0

Reorder the terms:
(6 + 3x)(6x + 5) = 0

Reorder the terms:
(6 + 3x)(5 + 6x) = 0

Multiply (6 + 3x) * (5 + 6x)
(6(5 + 6x) + 3x * (5 + 6x)) = 0
((5 * 6 + 6x * 6) + 3x * (5 + 6x)) = 0
((30 + 36x) + 3x * (5 + 6x)) = 0
(30 + 36x + (5 * 3x + 6x * 3x)) = 0
(30 + 36x + (15x + 18x2)) = 0

Combine like terms: 36x + 15x = 51x
(30 + 51x + 18x2) = 0

Solving
30 + 51x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 17x + 6x2) = 0

Factor a trinomial.
3((2 + x)(5 + 6x)) = 0

Ignore the factor 3.

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 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 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {-2, -0.8333333333}

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