(7x+6)(6x+8)=0

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Solution for (7x+6)(6x+8)=0 equation: 


Simplifying
(7x + 6)(6x + 8) = 0

Reorder the terms:
(6 + 7x)(6x + 8) = 0

Reorder the terms:
(6 + 7x)(8 + 6x) = 0

Multiply (6 + 7x) * (8 + 6x)
(6(8 + 6x) + 7x * (8 + 6x)) = 0
((8 * 6 + 6x * 6) + 7x * (8 + 6x)) = 0
((48 + 36x) + 7x * (8 + 6x)) = 0
(48 + 36x + (8 * 7x + 6x * 7x)) = 0
(48 + 36x + (56x + 42x2)) = 0

Combine like terms: 36x + 56x = 92x
(48 + 92x + 42x2) = 0

Solving
48 + 92x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 46x + 21x2) = 0

Factor a trinomial.
2((4 + 3x)(6 + 7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
6 + 7x = 0

Solving
6 + 7x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7x = 0 + -6

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

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

Divide each side by '7'.
x = -0.8571428571

Simplifying
x = -0.8571428571
Solution
x = {-1.333333333, -0.8571428571}

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