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

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

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

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

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

Multiply (-1 + 2x) * (3 + x)
(-1(3 + x) + 2x * (3 + x)) = (x + 7)(3 + -4x)
((3 * -1 + x * -1) + 2x * (3 + x)) = (x + 7)(3 + -4x)
((-3 + -1x) + 2x * (3 + x)) = (x + 7)(3 + -4x)
(-3 + -1x + (3 * 2x + x * 2x)) = (x + 7)(3 + -4x)
(-3 + -1x + (6x + 2x2)) = (x + 7)(3 + -4x)

Combine like terms: -1x + 6x = 5x
(-3 + 5x + 2x2) = (x + 7)(3 + -4x)

Reorder the terms:
-3 + 5x + 2x2 = (7 + x)(3 + -4x)

Multiply (7 + x) * (3 + -4x)
-3 + 5x + 2x2 = (7(3 + -4x) + x(3 + -4x))
-3 + 5x + 2x2 = ((3 * 7 + -4x * 7) + x(3 + -4x))
-3 + 5x + 2x2 = ((21 + -28x) + x(3 + -4x))
-3 + 5x + 2x2 = (21 + -28x + (3 * x + -4x * x))
-3 + 5x + 2x2 = (21 + -28x + (3x + -4x2))

Combine like terms: -28x + 3x = -25x
-3 + 5x + 2x2 = (21 + -25x + -4x2)

Solving
-3 + 5x + 2x2 = 21 + -25x + -4x2

Solving for variable 'x'.

Reorder the terms:
-3 + -21 + 5x + 25x + 2x2 + 4x2 = 21 + -25x + -4x2 + -21 + 25x + 4x2

Combine like terms: -3 + -21 = -24
-24 + 5x + 25x + 2x2 + 4x2 = 21 + -25x + -4x2 + -21 + 25x + 4x2

Combine like terms: 5x + 25x = 30x
-24 + 30x + 2x2 + 4x2 = 21 + -25x + -4x2 + -21 + 25x + 4x2

Combine like terms: 2x2 + 4x2 = 6x2
-24 + 30x + 6x2 = 21 + -25x + -4x2 + -21 + 25x + 4x2

Reorder the terms:
-24 + 30x + 6x2 = 21 + -21 + -25x + 25x + -4x2 + 4x2

Combine like terms: 21 + -21 = 0
-24 + 30x + 6x2 = 0 + -25x + 25x + -4x2 + 4x2
-24 + 30x + 6x2 = -25x + 25x + -4x2 + 4x2

Combine like terms: -25x + 25x = 0
-24 + 30x + 6x2 = 0 + -4x2 + 4x2
-24 + 30x + 6x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-24 + 30x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + 5x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-4 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + 5x + x2 = 0

Solving
-4 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 5x + x2 = 0 + 4

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

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

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 4 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5x + x2 = 10.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
x + 2.5 = 3.201562119

Simplifying
x + 2.5 = 3.201562119

Reorder the terms:
2.5 + x = 3.201562119

Solving
2.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.201562119 + -2.5
x = 3.201562119 + -2.5

Combine like terms: 3.201562119 + -2.5 = 0.701562119
x = 0.701562119

Simplifying
x = 0.701562119

Subproblem 2
x + 2.5 = -3.201562119

Simplifying
x + 2.5 = -3.201562119

Reorder the terms:
2.5 + x = -3.201562119

Solving
2.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.201562119 + -2.5
x = -3.201562119 + -2.5

Combine like terms: -3.201562119 + -2.5 = -5.701562119
x = -5.701562119

Simplifying
x = -5.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.701562119, -5.701562119}
Solution
x = {0.701562119, -5.701562119}