3(4x-5)2(11-2x)=43

Solution for 3(4x-5)2(11-2x)=43 equation:

Simplifying
3(4x + -5) * 2(11 + -2x) = 43

Reorder the terms:
3(-5 + 4x) * 2(11 + -2x) = 43

Reorder the terms for easier multiplication:
3 * 2(-5 + 4x)(11 + -2x) = 43

Multiply 3 * 2
6(-5 + 4x)(11 + -2x) = 43

Multiply (-5 + 4x) * (11 + -2x)
6(-5(11 + -2x) + 4x * (11 + -2x)) = 43
6((11 * -5 + -2x * -5) + 4x * (11 + -2x)) = 43
6((-55 + 10x) + 4x * (11 + -2x)) = 43
6(-55 + 10x + (11 * 4x + -2x * 4x)) = 43
6(-55 + 10x + (44x + -8x2)) = 43

Combine like terms: 10x + 44x = 54x
6(-55 + 54x + -8x2) = 43
(-55 * 6 + 54x * 6 + -8x2 * 6) = 43
(-330 + 324x + -48x2) = 43

Solving
-330 + 324x + -48x2 = 43

Solving for variable 'x'.

Reorder the terms:
-330 + -43 + 324x + -48x2 = 43 + -43

Combine like terms: -330 + -43 = -373
-373 + 324x + -48x2 = 43 + -43

Combine like terms: 43 + -43 = 0
-373 + 324x + -48x2 = 0

Begin completing the square.  Divide all terms by
-48 the coefficient of the squared term: 

Divide each side by '-48'.
7.770833333 + -6.75x + x2 = 0

Move the constant term to the right:

Add '-7.770833333' to each side of the equation.
7.770833333 + -6.75x + -7.770833333 + x2 = 0 + -7.770833333

Reorder the terms:
7.770833333 + -7.770833333 + -6.75x + x2 = 0 + -7.770833333

Combine like terms: 7.770833333 + -7.770833333 = 0.000000000
0.000000000 + -6.75x + x2 = 0 + -7.770833333
-6.75x + x2 = 0 + -7.770833333

Combine like terms: 0 + -7.770833333 = -7.770833333
-6.75x + x2 = -7.770833333

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = -7.770833333 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = -7.770833333 + 11.390625

Combine like terms: -7.770833333 + 11.390625 = 3.619791667
11.390625 + -6.75x + x2 = 3.619791667

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 3.619791667

Calculate the square root of the right side: 1.90257501

Break this problem into two subproblems by setting 
(x + -3.375) equal to 1.90257501 and -1.90257501.

Subproblem 1
x + -3.375 = 1.90257501

Simplifying
x + -3.375 = 1.90257501

Reorder the terms:
-3.375 + x = 1.90257501

Solving
-3.375 + x = 1.90257501

Solving for variable 'x'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + x = 1.90257501 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + x = 1.90257501 + 3.375
x = 1.90257501 + 3.375

Combine like terms: 1.90257501 + 3.375 = 5.27757501
x = 5.27757501

Simplifying
x = 5.27757501

Subproblem 2
x + -3.375 = -1.90257501

Simplifying
x + -3.375 = -1.90257501

Reorder the terms:
-3.375 + x = -1.90257501

Solving
-3.375 + x = -1.90257501

Solving for variable 'x'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + x = -1.90257501 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + x = -1.90257501 + 3.375
x = -1.90257501 + 3.375

Combine like terms: -1.90257501 + 3.375 = 1.47242499
x = 1.47242499

Simplifying
x = 1.47242499

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.27757501, 1.47242499}