(6x-7)(3x+9)=0

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Solution for (6x-7)(3x+9)=0 equation: 


Simplifying
(6x + -7)(3x + 9) = 0

Reorder the terms:
(-7 + 6x)(3x + 9) = 0

Reorder the terms:
(-7 + 6x)(9 + 3x) = 0

Multiply (-7 + 6x) * (9 + 3x)
(-7(9 + 3x) + 6x * (9 + 3x)) = 0
((9 * -7 + 3x * -7) + 6x * (9 + 3x)) = 0
((-63 + -21x) + 6x * (9 + 3x)) = 0
(-63 + -21x + (9 * 6x + 3x * 6x)) = 0
(-63 + -21x + (54x + 18x2)) = 0

Combine like terms: -21x + 54x = 33x
(-63 + 33x + 18x2) = 0

Solving
-63 + 33x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + 11x + 6x2) = 0

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

Ignore the factor 3.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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 = {-3, 1.166666667}

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