(3x-12)(11x-23)=0

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Solution for (3x-12)(11x-23)=0 equation: 


Simplifying
(3x + -12)(11x + -23) = 0

Reorder the terms:
(-12 + 3x)(11x + -23) = 0

Reorder the terms:
(-12 + 3x)(-23 + 11x) = 0

Multiply (-12 + 3x) * (-23 + 11x)
(-12(-23 + 11x) + 3x * (-23 + 11x)) = 0
((-23 * -12 + 11x * -12) + 3x * (-23 + 11x)) = 0
((276 + -132x) + 3x * (-23 + 11x)) = 0
(276 + -132x + (-23 * 3x + 11x * 3x)) = 0
(276 + -132x + (-69x + 33x2)) = 0

Combine like terms: -132x + -69x = -201x
(276 + -201x + 33x2) = 0

Solving
276 + -201x + 33x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(92 + -67x + 11x2) = 0

Factor a trinomial.
3((23 + -11x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(23 + -11x)' equal to zero and attempt to solve:

Simplifying
23 + -11x = 0

Solving
23 + -11x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -11x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -11x = 0 + -23
-11x = 0 + -23

Combine like terms: 0 + -23 = -23
-11x = -23

Divide each side by '-11'.
x = 2.090909091

Simplifying
x = 2.090909091

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2.090909091, 4}

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