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

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

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

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

Combine like terms: 3 + -1 = 2
2 + 4x = 2(2x + 2) * 2x

Reorder the terms:
2 + 4x = 2(2 + 2x) * 2x

Reorder the terms for easier multiplication:
2 + 4x = 2 * 2x(2 + 2x)

Multiply 2 * 2
2 + 4x = 4x(2 + 2x)
2 + 4x = (2 * 4x + 2x * 4x)
2 + 4x = (8x + 8x2)

Solving
2 + 4x = 8x + 8x2

Solving for variable 'x'.

Combine like terms: 4x + -8x = -4x
2 + -4x + -8x2 = 8x + 8x2 + -8x + -8x2

Reorder the terms:
2 + -4x + -8x2 = 8x + -8x + 8x2 + -8x2

Combine like terms: 8x + -8x = 0
2 + -4x + -8x2 = 0 + 8x2 + -8x2
2 + -4x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
2 + -4x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -2x + -4x2)' equal to zero and attempt to solve:

Simplifying
1 + -2x + -4x2 = 0

Solving
1 + -2x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.5x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.5x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.5x + x2 = 0 + 0.25
0.5x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.5x + x2 = 0.25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.25 + 0.0625

Combine like terms: 0.25 + 0.0625 = 0.3125
0.0625 + 0.5x + x2 = 0.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
x + 0.25 = 0.559016994

Simplifying
x + 0.25 = 0.559016994

Reorder the terms:
0.25 + x = 0.559016994

Solving
0.25 + x = 0.559016994

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.559016994 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.559016994 + -0.25
x = 0.559016994 + -0.25

Combine like terms: 0.559016994 + -0.25 = 0.309016994
x = 0.309016994

Simplifying
x = 0.309016994

Subproblem 2
x + 0.25 = -0.559016994

Simplifying
x + 0.25 = -0.559016994

Reorder the terms:
0.25 + x = -0.559016994

Solving
0.25 + x = -0.559016994

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.559016994 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.559016994 + -0.25
x = -0.559016994 + -0.25

Combine like terms: -0.559016994 + -0.25 = -0.809016994
x = -0.809016994

Simplifying
x = -0.809016994

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.309016994, -0.809016994}
Solution
x = {0.309016994, -0.809016994}