(3x+7)(6x+3)=0

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Solution for (3x+7)(6x+3)=0 equation: 


Simplifying
(3x + 7)(6x + 3) = 0

Reorder the terms:
(7 + 3x)(6x + 3) = 0

Reorder the terms:
(7 + 3x)(3 + 6x) = 0

Multiply (7 + 3x) * (3 + 6x)
(7(3 + 6x) + 3x * (3 + 6x)) = 0
((3 * 7 + 6x * 7) + 3x * (3 + 6x)) = 0
((21 + 42x) + 3x * (3 + 6x)) = 0
(21 + 42x + (3 * 3x + 6x * 3x)) = 0
(21 + 42x + (9x + 18x2)) = 0

Combine like terms: 42x + 9x = 51x
(21 + 51x + 18x2) = 0

Solving
21 + 51x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 17x + 6x2) = 0

Factor a trinomial.
3((7 + 3x)(1 + 2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2.333333333, -0.5}

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