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

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


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

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

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

Multiply (-7 + 3x) * (-3 + 3x)
(-7(-3 + 3x) + 3x * (-3 + 3x)) = 0
((-3 * -7 + 3x * -7) + 3x * (-3 + 3x)) = 0
((21 + -21x) + 3x * (-3 + 3x)) = 0
(21 + -21x + (-3 * 3x + 3x * 3x)) = 0
(21 + -21x + (-9x + 9x2)) = 0

Combine like terms: -21x + -9x = -30x
(21 + -30x + 9x2) = 0

Solving
21 + -30x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -10x + 3x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {1, 2.333333333}

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