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

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


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

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

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

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

Combine like terms: -18x + 21x = 3x
(-21 + 3x + 18x2) = 0

Solving
-21 + 3x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + x + 6x2) = 0

Factor a trinomial.
3((-7 + -6x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.166666667, 1}

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