(11x-5)(3x-2)12=2352

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Solution for (11x-5)(3x-2)12=2352 equation: 


Simplifying
(11x + -5)(3x + -2) * 12 = 2352

Reorder the terms:
(-5 + 11x)(3x + -2) * 12 = 2352

Reorder the terms:
(-5 + 11x)(-2 + 3x) * 12 = 2352

Reorder the terms for easier multiplication:
12(-5 + 11x)(-2 + 3x) = 2352

Multiply (-5 + 11x) * (-2 + 3x)
12(-5(-2 + 3x) + 11x * (-2 + 3x)) = 2352
12((-2 * -5 + 3x * -5) + 11x * (-2 + 3x)) = 2352
12((10 + -15x) + 11x * (-2 + 3x)) = 2352
12(10 + -15x + (-2 * 11x + 3x * 11x)) = 2352
12(10 + -15x + (-22x + 33x2)) = 2352

Combine like terms: -15x + -22x = -37x
12(10 + -37x + 33x2) = 2352
(10 * 12 + -37x * 12 + 33x2 * 12) = 2352
(120 + -444x + 396x2) = 2352

Solving
120 + -444x + 396x2 = 2352

Solving for variable 'x'.

Reorder the terms:
120 + -2352 + -444x + 396x2 = 2352 + -2352

Combine like terms: 120 + -2352 = -2232
-2232 + -444x + 396x2 = 2352 + -2352

Combine like terms: 2352 + -2352 = 0
-2232 + -444x + 396x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-186 + -37x + 33x2) = 0

Factor a trinomial.
12((-62 + -33x)(3 + -1x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-62 + -33x)' equal to zero and attempt to solve:

Simplifying
-62 + -33x = 0

Solving
-62 + -33x = 0

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

Add '62' to each side of the equation.
-62 + 62 + -33x = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -33x = 0 + 62
-33x = 0 + 62

Combine like terms: 0 + 62 = 62
-33x = 62

Divide each side by '-33'.
x = -1.878787879

Simplifying
x = -1.878787879

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 = {-1.878787879, 3}

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