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

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

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

Reorder the terms:
2x(-3 + 2x) = 4 + -5(x)
(-3 * 2x + 2x * 2x) = 4 + -5(x)
(-6x + 4x2) = 4 + -5(x)

Solving
-6x + 4x2 = 4 + -5x

Solving for variable 'x'.

Reorder the terms:
-4 + -6x + 5x + 4x2 = 4 + -5x + -4 + 5x

Combine like terms: -6x + 5x = -1x
-4 + -1x + 4x2 = 4 + -5x + -4 + 5x

Reorder the terms:
-4 + -1x + 4x2 = 4 + -4 + -5x + 5x

Combine like terms: 4 + -4 = 0
-4 + -1x + 4x2 = 0 + -5x + 5x
-4 + -1x + 4x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-4 + -1x + 4x2 = 0

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

Divide each side by '4'.
-1 + -0.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.25x + x2 = 0 + 1
-0.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.25x + x2 = 1

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 1 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 1 + 0.015625

Combine like terms: 1 + 0.015625 = 1.015625
0.015625 + -0.25x + x2 = 1.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.007782219 and -1.007782219.

Subproblem 1
x + -0.125 = 1.007782219

Simplifying
x + -0.125 = 1.007782219

Reorder the terms:
-0.125 + x = 1.007782219

Solving
-0.125 + x = 1.007782219

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 1.007782219 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 1.007782219 + 0.125
x = 1.007782219 + 0.125

Combine like terms: 1.007782219 + 0.125 = 1.132782219
x = 1.132782219

Simplifying
x = 1.132782219

Subproblem 2
x + -0.125 = -1.007782219

Simplifying
x + -0.125 = -1.007782219

Reorder the terms:
-0.125 + x = -1.007782219

Solving
-0.125 + x = -1.007782219

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -1.007782219 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -1.007782219 + 0.125
x = -1.007782219 + 0.125

Combine like terms: -1.007782219 + 0.125 = -0.882782219
x = -0.882782219

Simplifying
x = -0.882782219

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.132782219, -0.882782219}