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

Solution for 7(x+3)-4(2-x)=5(2x-3)(2x+1) equation:

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

Reorder the terms:
7(3 + x) + -4(2 + -1x) = 5(2x + -3)(2x + 1)
(3 * 7 + x * 7) + -4(2 + -1x) = 5(2x + -3)(2x + 1)
(21 + 7x) + -4(2 + -1x) = 5(2x + -3)(2x + 1)
21 + 7x + (2 * -4 + -1x * -4) = 5(2x + -3)(2x + 1)
21 + 7x + (-8 + 4x) = 5(2x + -3)(2x + 1)

Reorder the terms:
21 + -8 + 7x + 4x = 5(2x + -3)(2x + 1)

Combine like terms: 21 + -8 = 13
13 + 7x + 4x = 5(2x + -3)(2x + 1)

Combine like terms: 7x + 4x = 11x
13 + 11x = 5(2x + -3)(2x + 1)

Reorder the terms:
13 + 11x = 5(-3 + 2x)(2x + 1)

Reorder the terms:
13 + 11x = 5(-3 + 2x)(1 + 2x)

Multiply (-3 + 2x) * (1 + 2x)
13 + 11x = 5(-3(1 + 2x) + 2x * (1 + 2x))
13 + 11x = 5((1 * -3 + 2x * -3) + 2x * (1 + 2x))
13 + 11x = 5((-3 + -6x) + 2x * (1 + 2x))
13 + 11x = 5(-3 + -6x + (1 * 2x + 2x * 2x))
13 + 11x = 5(-3 + -6x + (2x + 4x2))

Combine like terms: -6x + 2x = -4x
13 + 11x = 5(-3 + -4x + 4x2)
13 + 11x = (-3 * 5 + -4x * 5 + 4x2 * 5)
13 + 11x = (-15 + -20x + 20x2)

Solving
13 + 11x = -15 + -20x + 20x2

Solving for variable 'x'.

Reorder the terms:
13 + 15 + 11x + 20x + -20x2 = -15 + -20x + 20x2 + 15 + 20x + -20x2

Combine like terms: 13 + 15 = 28
28 + 11x + 20x + -20x2 = -15 + -20x + 20x2 + 15 + 20x + -20x2

Combine like terms: 11x + 20x = 31x
28 + 31x + -20x2 = -15 + -20x + 20x2 + 15 + 20x + -20x2

Reorder the terms:
28 + 31x + -20x2 = -15 + 15 + -20x + 20x + 20x2 + -20x2

Combine like terms: -15 + 15 = 0
28 + 31x + -20x2 = 0 + -20x + 20x + 20x2 + -20x2
28 + 31x + -20x2 = -20x + 20x + 20x2 + -20x2

Combine like terms: -20x + 20x = 0
28 + 31x + -20x2 = 0 + 20x2 + -20x2
28 + 31x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
28 + 31x + -20x2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-1.4 + -1.55x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + -1.55x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + -1.55x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + -1.55x + x2 = 0 + 1.4
-1.55x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
-1.55x + x2 = 1.4

The x term is -1.55x.  Take half its coefficient (-0.775).
Square it (0.600625) and add it to both sides.

Add '0.600625' to each side of the equation.
-1.55x + 0.600625 + x2 = 1.4 + 0.600625

Reorder the terms:
0.600625 + -1.55x + x2 = 1.4 + 0.600625

Combine like terms: 1.4 + 0.600625 = 2.000625
0.600625 + -1.55x + x2 = 2.000625

Factor a perfect square on the left side:
(x + -0.775)(x + -0.775) = 2.000625

Calculate the square root of the right side: 1.414434516

Break this problem into two subproblems by setting 
(x + -0.775) equal to 1.414434516 and -1.414434516.

Subproblem 1
x + -0.775 = 1.414434516

Simplifying
x + -0.775 = 1.414434516

Reorder the terms:
-0.775 + x = 1.414434516

Solving
-0.775 + x = 1.414434516

Solving for variable 'x'.

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

Add '0.775' to each side of the equation.
-0.775 + 0.775 + x = 1.414434516 + 0.775

Combine like terms: -0.775 + 0.775 = 0.000
0.000 + x = 1.414434516 + 0.775
x = 1.414434516 + 0.775

Combine like terms: 1.414434516 + 0.775 = 2.189434516
x = 2.189434516

Simplifying
x = 2.189434516

Subproblem 2
x + -0.775 = -1.414434516

Simplifying
x + -0.775 = -1.414434516

Reorder the terms:
-0.775 + x = -1.414434516

Solving
-0.775 + x = -1.414434516

Solving for variable 'x'.

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

Add '0.775' to each side of the equation.
-0.775 + 0.775 + x = -1.414434516 + 0.775

Combine like terms: -0.775 + 0.775 = 0.000
0.000 + x = -1.414434516 + 0.775
x = -1.414434516 + 0.775

Combine like terms: -1.414434516 + 0.775 = -0.639434516
x = -0.639434516

Simplifying
x = -0.639434516

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.189434516, -0.639434516}