5(x-4)2(x+1)=3(2-4x)

Solution for 5(x-4)2(x+1)=3(2-4x) equation:

Simplifying
5(x + -4) * 2(x + 1) = 3(2 + -4x)

Reorder the terms:
5(-4 + x) * 2(x + 1) = 3(2 + -4x)

Reorder the terms:
5(-4 + x) * 2(1 + x) = 3(2 + -4x)

Reorder the terms for easier multiplication:
5 * 2(-4 + x)(1 + x) = 3(2 + -4x)

Multiply 5 * 2
10(-4 + x)(1 + x) = 3(2 + -4x)

Multiply (-4 + x) * (1 + x)
10(-4(1 + x) + x(1 + x)) = 3(2 + -4x)
10((1 * -4 + x * -4) + x(1 + x)) = 3(2 + -4x)
10((-4 + -4x) + x(1 + x)) = 3(2 + -4x)
10(-4 + -4x + (1 * x + x * x)) = 3(2 + -4x)
10(-4 + -4x + (1x + x2)) = 3(2 + -4x)

Combine like terms: -4x + 1x = -3x
10(-4 + -3x + x2) = 3(2 + -4x)
(-4 * 10 + -3x * 10 + x2 * 10) = 3(2 + -4x)
(-40 + -30x + 10x2) = 3(2 + -4x)
-40 + -30x + 10x2 = (2 * 3 + -4x * 3)
-40 + -30x + 10x2 = (6 + -12x)

Solving
-40 + -30x + 10x2 = 6 + -12x

Solving for variable 'x'.

Reorder the terms:
-40 + -6 + -30x + 12x + 10x2 = 6 + -12x + -6 + 12x

Combine like terms: -40 + -6 = -46
-46 + -30x + 12x + 10x2 = 6 + -12x + -6 + 12x

Combine like terms: -30x + 12x = -18x
-46 + -18x + 10x2 = 6 + -12x + -6 + 12x

Reorder the terms:
-46 + -18x + 10x2 = 6 + -6 + -12x + 12x

Combine like terms: 6 + -6 = 0
-46 + -18x + 10x2 = 0 + -12x + 12x
-46 + -18x + 10x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-46 + -18x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-23 + -9x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-23 + -9x + 5x2)' equal to zero and attempt to solve:

Simplifying
-23 + -9x + 5x2 = 0

Solving
-23 + -9x + 5x2 = 0

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

Divide each side by '5'.
-4.6 + -1.8x + x2 = 0

Move the constant term to the right:

Add '4.6' to each side of the equation.
-4.6 + -1.8x + 4.6 + x2 = 0 + 4.6

Reorder the terms:
-4.6 + 4.6 + -1.8x + x2 = 0 + 4.6

Combine like terms: -4.6 + 4.6 = 0.0
0.0 + -1.8x + x2 = 0 + 4.6
-1.8x + x2 = 0 + 4.6

Combine like terms: 0 + 4.6 = 4.6
-1.8x + x2 = 4.6

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = 4.6 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = 4.6 + 0.81

Combine like terms: 4.6 + 0.81 = 5.41
0.81 + -1.8x + x2 = 5.41

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 5.41

Calculate the square root of the right side: 2.32594067

Break this problem into two subproblems by setting 
(x + -0.9) equal to 2.32594067 and -2.32594067.

Subproblem 1
x + -0.9 = 2.32594067

Simplifying
x + -0.9 = 2.32594067

Reorder the terms:
-0.9 + x = 2.32594067

Solving
-0.9 + x = 2.32594067

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = 2.32594067 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = 2.32594067 + 0.9
x = 2.32594067 + 0.9

Combine like terms: 2.32594067 + 0.9 = 3.22594067
x = 3.22594067

Simplifying
x = 3.22594067

Subproblem 2
x + -0.9 = -2.32594067

Simplifying
x + -0.9 = -2.32594067

Reorder the terms:
-0.9 + x = -2.32594067

Solving
-0.9 + x = -2.32594067

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = -2.32594067 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = -2.32594067 + 0.9
x = -2.32594067 + 0.9

Combine like terms: -2.32594067 + 0.9 = -1.42594067
x = -1.42594067

Simplifying
x = -1.42594067

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.22594067, -1.42594067}
Solution
x = {3.22594067, -1.42594067}