(3x-3)(3x-4)=0

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Solution for (3x-3)(3x-4)=0 equation: 


Simplifying
(3x + -3)(3x + -4) = 0

Reorder the terms:
(-3 + 3x)(3x + -4) = 0

Reorder the terms:
(-3 + 3x)(-4 + 3x) = 0

Multiply (-3 + 3x) * (-4 + 3x)
(-3(-4 + 3x) + 3x * (-4 + 3x)) = 0
((-4 * -3 + 3x * -3) + 3x * (-4 + 3x)) = 0
((12 + -9x) + 3x * (-4 + 3x)) = 0
(12 + -9x + (-4 * 3x + 3x * 3x)) = 0
(12 + -9x + (-12x + 9x2)) = 0

Combine like terms: -9x + -12x = -21x
(12 + -21x + 9x2) = 0

Solving
12 + -21x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -7x + 3x2) = 0

Factor a trinomial.
3((1 + -1x)(4 + -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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {1, 1.333333333}

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