(3x+8)(6x-7)=0

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Solution for (3x+8)(6x-7)=0 equation: 


Simplifying
(3x + 8)(6x + -7) = 0

Reorder the terms:
(8 + 3x)(6x + -7) = 0

Reorder the terms:
(8 + 3x)(-7 + 6x) = 0

Multiply (8 + 3x) * (-7 + 6x)
(8(-7 + 6x) + 3x * (-7 + 6x)) = 0
((-7 * 8 + 6x * 8) + 3x * (-7 + 6x)) = 0
((-56 + 48x) + 3x * (-7 + 6x)) = 0
(-56 + 48x + (-7 * 3x + 6x * 3x)) = 0
(-56 + 48x + (-21x + 18x2)) = 0

Combine like terms: 48x + -21x = 27x
(-56 + 27x + 18x2) = 0

Solving
-56 + 27x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -3x)(7 + -6x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

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 = {-2.666666667, 1.166666667}

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