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

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

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

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

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

Multiply (-1 + 4x) * (3 + 2x)
4(-1(3 + 2x) + 4x * (3 + 2x)) = (x + 3)(x + -1)
4((3 * -1 + 2x * -1) + 4x * (3 + 2x)) = (x + 3)(x + -1)
4((-3 + -2x) + 4x * (3 + 2x)) = (x + 3)(x + -1)
4(-3 + -2x + (3 * 4x + 2x * 4x)) = (x + 3)(x + -1)
4(-3 + -2x + (12x + 8x2)) = (x + 3)(x + -1)

Combine like terms: -2x + 12x = 10x
4(-3 + 10x + 8x2) = (x + 3)(x + -1)
(-3 * 4 + 10x * 4 + 8x2 * 4) = (x + 3)(x + -1)
(-12 + 40x + 32x2) = (x + 3)(x + -1)

Reorder the terms:
-12 + 40x + 32x2 = (3 + x)(x + -1)

Reorder the terms:
-12 + 40x + 32x2 = (3 + x)(-1 + x)

Multiply (3 + x) * (-1 + x)
-12 + 40x + 32x2 = (3(-1 + x) + x(-1 + x))
-12 + 40x + 32x2 = ((-1 * 3 + x * 3) + x(-1 + x))
-12 + 40x + 32x2 = ((-3 + 3x) + x(-1 + x))
-12 + 40x + 32x2 = (-3 + 3x + (-1 * x + x * x))
-12 + 40x + 32x2 = (-3 + 3x + (-1x + x2))

Combine like terms: 3x + -1x = 2x
-12 + 40x + 32x2 = (-3 + 2x + x2)

Solving
-12 + 40x + 32x2 = -3 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + 3 + 40x + -2x + 32x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: -12 + 3 = -9
-9 + 40x + -2x + 32x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: 40x + -2x = 38x
-9 + 38x + 32x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: 32x2 + -1x2 = 31x2
-9 + 38x + 31x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Reorder the terms:
-9 + 38x + 31x2 = -3 + 3 + 2x + -2x + x2 + -1x2

Combine like terms: -3 + 3 = 0
-9 + 38x + 31x2 = 0 + 2x + -2x + x2 + -1x2
-9 + 38x + 31x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-9 + 38x + 31x2 = 0 + x2 + -1x2
-9 + 38x + 31x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + 38x + 31x2 = 0

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

Divide each side by '31'.
-0.2903225806 + 1.225806452x + x2 = 0

Move the constant term to the right:

Add '0.2903225806' to each side of the equation.
-0.2903225806 + 1.225806452x + 0.2903225806 + x2 = 0 + 0.2903225806

Reorder the terms:
-0.2903225806 + 0.2903225806 + 1.225806452x + x2 = 0 + 0.2903225806

Combine like terms: -0.2903225806 + 0.2903225806 = 0.0000000000
0.0000000000 + 1.225806452x + x2 = 0 + 0.2903225806
1.225806452x + x2 = 0 + 0.2903225806

Combine like terms: 0 + 0.2903225806 = 0.2903225806
1.225806452x + x2 = 0.2903225806

The x term is 1.225806452x.  Take half its coefficient (0.612903226).
Square it (0.3756503644) and add it to both sides.

Add '0.3756503644' to each side of the equation.
1.225806452x + 0.3756503644 + x2 = 0.2903225806 + 0.3756503644

Reorder the terms:
0.3756503644 + 1.225806452x + x2 = 0.2903225806 + 0.3756503644

Combine like terms: 0.2903225806 + 0.3756503644 = 0.665972945
0.3756503644 + 1.225806452x + x2 = 0.665972945

Factor a perfect square on the left side:
(x + 0.612903226)(x + 0.612903226) = 0.665972945

Calculate the square root of the right side: 0.816071654

Break this problem into two subproblems by setting 
(x + 0.612903226) equal to 0.816071654 and -0.816071654.

Subproblem 1
x + 0.612903226 = 0.816071654

Simplifying
x + 0.612903226 = 0.816071654

Reorder the terms:
0.612903226 + x = 0.816071654

Solving
0.612903226 + x = 0.816071654

Solving for variable 'x'.

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

Add '-0.612903226' to each side of the equation.
0.612903226 + -0.612903226 + x = 0.816071654 + -0.612903226

Combine like terms: 0.612903226 + -0.612903226 = 0.000000000
0.000000000 + x = 0.816071654 + -0.612903226
x = 0.816071654 + -0.612903226

Combine like terms: 0.816071654 + -0.612903226 = 0.203168428
x = 0.203168428

Simplifying
x = 0.203168428

Subproblem 2
x + 0.612903226 = -0.816071654

Simplifying
x + 0.612903226 = -0.816071654

Reorder the terms:
0.612903226 + x = -0.816071654

Solving
0.612903226 + x = -0.816071654

Solving for variable 'x'.

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

Add '-0.612903226' to each side of the equation.
0.612903226 + -0.612903226 + x = -0.816071654 + -0.612903226

Combine like terms: 0.612903226 + -0.612903226 = 0.000000000
0.000000000 + x = -0.816071654 + -0.612903226
x = -0.816071654 + -0.612903226

Combine like terms: -0.816071654 + -0.612903226 = -1.42897488
x = -1.42897488

Simplifying
x = -1.42897488

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.203168428, -1.42897488}