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

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


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

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

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

Multiply (-6 + 9x) * (-9 + 7x)
(-6(-9 + 7x) + 9x * (-9 + 7x)) = 0
((-9 * -6 + 7x * -6) + 9x * (-9 + 7x)) = 0
((54 + -42x) + 9x * (-9 + 7x)) = 0
(54 + -42x + (-9 * 9x + 7x * 9x)) = 0
(54 + -42x + (-81x + 63x2)) = 0

Combine like terms: -42x + -81x = -123x
(54 + -123x + 63x2) = 0

Solving
54 + -123x + 63x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -41x + 21x2) = 0

Factor a trinomial.
3((2 + -3x)(9 + -7x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(9 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Divide each side by '-7'.
x = 1.285714286

Simplifying
x = 1.285714286
Solution
x = {0.6666666667, 1.285714286}

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