(2x+3)(6x+7)=0

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Solution for (2x+3)(6x+7)=0 equation: 


Simplifying
(2x + 3)(6x + 7) = 0

Reorder the terms:
(3 + 2x)(6x + 7) = 0

Reorder the terms:
(3 + 2x)(7 + 6x) = 0

Multiply (3 + 2x) * (7 + 6x)
(3(7 + 6x) + 2x * (7 + 6x)) = 0
((7 * 3 + 6x * 3) + 2x * (7 + 6x)) = 0
((21 + 18x) + 2x * (7 + 6x)) = 0
(21 + 18x + (7 * 2x + 6x * 2x)) = 0
(21 + 18x + (14x + 12x2)) = 0

Combine like terms: 18x + 14x = 32x
(21 + 32x + 12x2) = 0

Solving
21 + 32x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 2x)(7 + 6x) = 0


Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(7 + 6x)' equal to zero and attempt to solve:

Simplifying
7 + 6x = 0

Solving
7 + 6x = 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 + 6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6x = 0 + -7
6x = 0 + -7

Combine like terms: 0 + -7 = -7
6x = -7

Divide each side by '6'.
x = -1.166666667

Simplifying
x = -1.166666667
Solution
x = {-1.5, -1.166666667}

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