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

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

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

Multiply (5 + 2x) * (7 + -4x)
(5(7 + -4x) + 2x * (7 + -4x)) = (4x + -3)(3x + 3)
((7 * 5 + -4x * 5) + 2x * (7 + -4x)) = (4x + -3)(3x + 3)
((35 + -20x) + 2x * (7 + -4x)) = (4x + -3)(3x + 3)
(35 + -20x + (7 * 2x + -4x * 2x)) = (4x + -3)(3x + 3)
(35 + -20x + (14x + -8x2)) = (4x + -3)(3x + 3)

Combine like terms: -20x + 14x = -6x
(35 + -6x + -8x2) = (4x + -3)(3x + 3)

Reorder the terms:
35 + -6x + -8x2 = (-3 + 4x)(3x + 3)

Reorder the terms:
35 + -6x + -8x2 = (-3 + 4x)(3 + 3x)

Multiply (-3 + 4x) * (3 + 3x)
35 + -6x + -8x2 = (-3(3 + 3x) + 4x * (3 + 3x))
35 + -6x + -8x2 = ((3 * -3 + 3x * -3) + 4x * (3 + 3x))
35 + -6x + -8x2 = ((-9 + -9x) + 4x * (3 + 3x))
35 + -6x + -8x2 = (-9 + -9x + (3 * 4x + 3x * 4x))
35 + -6x + -8x2 = (-9 + -9x + (12x + 12x2))

Combine like terms: -9x + 12x = 3x
35 + -6x + -8x2 = (-9 + 3x + 12x2)

Solving
35 + -6x + -8x2 = -9 + 3x + 12x2

Solving for variable 'x'.

Reorder the terms:
35 + 9 + -6x + -3x + -8x2 + -12x2 = -9 + 3x + 12x2 + 9 + -3x + -12x2

Combine like terms: 35 + 9 = 44
44 + -6x + -3x + -8x2 + -12x2 = -9 + 3x + 12x2 + 9 + -3x + -12x2

Combine like terms: -6x + -3x = -9x
44 + -9x + -8x2 + -12x2 = -9 + 3x + 12x2 + 9 + -3x + -12x2

Combine like terms: -8x2 + -12x2 = -20x2
44 + -9x + -20x2 = -9 + 3x + 12x2 + 9 + -3x + -12x2

Reorder the terms:
44 + -9x + -20x2 = -9 + 9 + 3x + -3x + 12x2 + -12x2

Combine like terms: -9 + 9 = 0
44 + -9x + -20x2 = 0 + 3x + -3x + 12x2 + -12x2
44 + -9x + -20x2 = 3x + -3x + 12x2 + -12x2

Combine like terms: 3x + -3x = 0
44 + -9x + -20x2 = 0 + 12x2 + -12x2
44 + -9x + -20x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
44 + -9x + -20x2 = 0

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

Divide each side by '-20'.
-2.2 + 0.45x + x2 = 0.0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + 0.45x + 2.2 + x2 = 0.0 + 2.2

Reorder the terms:
-2.2 + 2.2 + 0.45x + x2 = 0.0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + 0.45x + x2 = 0.0 + 2.2
0.45x + x2 = 0.0 + 2.2

Combine like terms: 0.0 + 2.2 = 2.2
0.45x + x2 = 2.2

The x term is 0.45x.  Take half its coefficient (0.225).
Square it (0.050625) and add it to both sides.

Add '0.050625' to each side of the equation.
0.45x + 0.050625 + x2 = 2.2 + 0.050625

Reorder the terms:
0.050625 + 0.45x + x2 = 2.2 + 0.050625

Combine like terms: 2.2 + 0.050625 = 2.250625
0.050625 + 0.45x + x2 = 2.250625

Factor a perfect square on the left side:
(x + 0.225)(x + 0.225) = 2.250625

Calculate the square root of the right side: 1.500208319

Break this problem into two subproblems by setting 
(x + 0.225) equal to 1.500208319 and -1.500208319.

Subproblem 1
x + 0.225 = 1.500208319

Simplifying
x + 0.225 = 1.500208319

Reorder the terms:
0.225 + x = 1.500208319

Solving
0.225 + x = 1.500208319

Solving for variable 'x'.

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

Add '-0.225' to each side of the equation.
0.225 + -0.225 + x = 1.500208319 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + x = 1.500208319 + -0.225
x = 1.500208319 + -0.225

Combine like terms: 1.500208319 + -0.225 = 1.275208319
x = 1.275208319

Simplifying
x = 1.275208319

Subproblem 2
x + 0.225 = -1.500208319

Simplifying
x + 0.225 = -1.500208319

Reorder the terms:
0.225 + x = -1.500208319

Solving
0.225 + x = -1.500208319

Solving for variable 'x'.

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

Add '-0.225' to each side of the equation.
0.225 + -0.225 + x = -1.500208319 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + x = -1.500208319 + -0.225
x = -1.500208319 + -0.225

Combine like terms: -1.500208319 + -0.225 = -1.725208319
x = -1.725208319

Simplifying
x = -1.725208319

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.275208319, -1.725208319}