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

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


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

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

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

Multiply (7 + 3x) * (-7 + 6x)
(7(-7 + 6x) + 3x * (-7 + 6x)) = 0
((-7 * 7 + 6x * 7) + 3x * (-7 + 6x)) = 0
((-49 + 42x) + 3x * (-7 + 6x)) = 0
(-49 + 42x + (-7 * 3x + 6x * 3x)) = 0
(-49 + 42x + (-21x + 18x2)) = 0

Combine like terms: 42x + -21x = 21x
(-49 + 21x + 18x2) = 0

Solving
-49 + 21x + 18x2 = 0

Solving for variable 'x'.

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


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 '(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 = {-2.333333333, 1.166666667}

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