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

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


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

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

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

Multiply (-6 + 3x) * (7 + 6x)
(-6(7 + 6x) + 3x * (7 + 6x)) = 0
((7 * -6 + 6x * -6) + 3x * (7 + 6x)) = 0
((-42 + -36x) + 3x * (7 + 6x)) = 0
(-42 + -36x + (7 * 3x + 6x * 3x)) = 0
(-42 + -36x + (21x + 18x2)) = 0

Combine like terms: -36x + 21x = -15x
(-42 + -15x + 18x2) = 0

Solving
-42 + -15x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -5x + 6x2) = 0

Factor a trinomial.
3((-7 + -6x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.166666667, 2}

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