4(x-1)13x=-2x-4+3x

Solution for 4(x-1)13x=-2x-4+3x equation:

Simplifying
4(x + -1) * 13x = -2x + -4 + 3x

Reorder the terms:
4(-1 + x) * 13x = -2x + -4 + 3x

Reorder the terms for easier multiplication:
4 * 13x(-1 + x) = -2x + -4 + 3x

Multiply 4 * 13
52x(-1 + x) = -2x + -4 + 3x
(-1 * 52x + x * 52x) = -2x + -4 + 3x
(-52x + 52x2) = -2x + -4 + 3x

Reorder the terms:
-52x + 52x2 = -4 + -2x + 3x

Combine like terms: -2x + 3x = 1x
-52x + 52x2 = -4 + 1x

Solving
-52x + 52x2 = -4 + 1x

Solving for variable 'x'.

Reorder the terms:
4 + -52x + -1x + 52x2 = -4 + 1x + 4 + -1x

Combine like terms: -52x + -1x = -53x
4 + -53x + 52x2 = -4 + 1x + 4 + -1x

Reorder the terms:
4 + -53x + 52x2 = -4 + 4 + 1x + -1x

Combine like terms: -4 + 4 = 0
4 + -53x + 52x2 = 0 + 1x + -1x
4 + -53x + 52x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
4 + -53x + 52x2 = 0

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

Divide each side by '52'.
0.07692307692 + -1.019230769x + x2 = 0

Move the constant term to the right:

Add '-0.07692307692' to each side of the equation.
0.07692307692 + -1.019230769x + -0.07692307692 + x2 = 0 + -0.07692307692

Reorder the terms:
0.07692307692 + -0.07692307692 + -1.019230769x + x2 = 0 + -0.07692307692

Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000
0.00000000000 + -1.019230769x + x2 = 0 + -0.07692307692
-1.019230769x + x2 = 0 + -0.07692307692

Combine like terms: 0 + -0.07692307692 = -0.07692307692
-1.019230769x + x2 = -0.07692307692

The x term is -1.019230769x.  Take half its coefficient (-0.5096153845).
Square it (0.2597078401) and add it to both sides.

Add '0.2597078401' to each side of the equation.
-1.019230769x + 0.2597078401 + x2 = -0.07692307692 + 0.2597078401

Reorder the terms:
0.2597078401 + -1.019230769x + x2 = -0.07692307692 + 0.2597078401

Combine like terms: -0.07692307692 + 0.2597078401 = 0.18278476318
0.2597078401 + -1.019230769x + x2 = 0.18278476318

Factor a perfect square on the left side:
(x + -0.5096153845)(x + -0.5096153845) = 0.18278476318

Calculate the square root of the right side: 0.427533347

Break this problem into two subproblems by setting 
(x + -0.5096153845) equal to 0.427533347 and -0.427533347.

Subproblem 1
x + -0.5096153845 = 0.427533347

Simplifying
x + -0.5096153845 = 0.427533347

Reorder the terms:
-0.5096153845 + x = 0.427533347

Solving
-0.5096153845 + x = 0.427533347

Solving for variable 'x'.

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

Add '0.5096153845' to each side of the equation.
-0.5096153845 + 0.5096153845 + x = 0.427533347 + 0.5096153845

Combine like terms: -0.5096153845 + 0.5096153845 = 0.0000000000
0.0000000000 + x = 0.427533347 + 0.5096153845
x = 0.427533347 + 0.5096153845

Combine like terms: 0.427533347 + 0.5096153845 = 0.9371487315
x = 0.9371487315

Simplifying
x = 0.9371487315

Subproblem 2
x + -0.5096153845 = -0.427533347

Simplifying
x + -0.5096153845 = -0.427533347

Reorder the terms:
-0.5096153845 + x = -0.427533347

Solving
-0.5096153845 + x = -0.427533347

Solving for variable 'x'.

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

Add '0.5096153845' to each side of the equation.
-0.5096153845 + 0.5096153845 + x = -0.427533347 + 0.5096153845

Combine like terms: -0.5096153845 + 0.5096153845 = 0.0000000000
0.0000000000 + x = -0.427533347 + 0.5096153845
x = -0.427533347 + 0.5096153845

Combine like terms: -0.427533347 + 0.5096153845 = 0.0820820375
x = 0.0820820375

Simplifying
x = 0.0820820375

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9371487315, 0.0820820375}