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

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


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

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

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

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

Combine like terms: 18x + 63x = 81x
(-21 + 81x + -54x2) = 0

Solving
-21 + 81x + -54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 27x + -18x2) = 0

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {1.166666667, 0.3333333333}

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