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

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

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

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

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

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

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

Solving
54 + -81x + 21x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x = 0 + -6
-7x = 0 + -6

Combine like terms: 0 + -6 = -6
-7x = -6

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
Subproblem 2
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
Solution
x = {0.8571428571, 3}