(3x-6)(4x-3)=0

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Solution for (3x-6)(4x-3)=0 equation: 


Simplifying
(3x + -6)(4x + -3) = 0

Reorder the terms:
(-6 + 3x)(4x + -3) = 0

Reorder the terms:
(-6 + 3x)(-3 + 4x) = 0

Multiply (-6 + 3x) * (-3 + 4x)
(-6(-3 + 4x) + 3x * (-3 + 4x)) = 0
((-3 * -6 + 4x * -6) + 3x * (-3 + 4x)) = 0
((18 + -24x) + 3x * (-3 + 4x)) = 0
(18 + -24x + (-3 * 3x + 4x * 3x)) = 0
(18 + -24x + (-9x + 12x2)) = 0

Combine like terms: -24x + -9x = -33x
(18 + -33x + 12x2) = 0

Solving
18 + -33x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -11x + 4x2) = 0

Factor a trinomial.
3((3 + -4x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.75, 2}

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