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

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

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

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

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

Multiply (2 + x) * (5 + -3x)
4(2(5 + -3x) + x(5 + -3x)) = 2x + -7
4((5 * 2 + -3x * 2) + x(5 + -3x)) = 2x + -7
4((10 + -6x) + x(5 + -3x)) = 2x + -7
4(10 + -6x + (5 * x + -3x * x)) = 2x + -7
4(10 + -6x + (5x + -3x2)) = 2x + -7

Combine like terms: -6x + 5x = -1x
4(10 + -1x + -3x2) = 2x + -7
(10 * 4 + -1x * 4 + -3x2 * 4) = 2x + -7
(40 + -4x + -12x2) = 2x + -7

Reorder the terms:
40 + -4x + -12x2 = -7 + 2x

Solving
40 + -4x + -12x2 = -7 + 2x

Solving for variable 'x'.

Reorder the terms:
40 + 7 + -4x + -2x + -12x2 = -7 + 2x + 7 + -2x

Combine like terms: 40 + 7 = 47
47 + -4x + -2x + -12x2 = -7 + 2x + 7 + -2x

Combine like terms: -4x + -2x = -6x
47 + -6x + -12x2 = -7 + 2x + 7 + -2x

Reorder the terms:
47 + -6x + -12x2 = -7 + 7 + 2x + -2x

Combine like terms: -7 + 7 = 0
47 + -6x + -12x2 = 0 + 2x + -2x
47 + -6x + -12x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
47 + -6x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-3.916666667 + 0.5x + x2 = 0

Move the constant term to the right:

Add '3.916666667' to each side of the equation.
-3.916666667 + 0.5x + 3.916666667 + x2 = 0 + 3.916666667

Reorder the terms:
-3.916666667 + 3.916666667 + 0.5x + x2 = 0 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + 0.5x + x2 = 0 + 3.916666667
0.5x + x2 = 0 + 3.916666667

Combine like terms: 0 + 3.916666667 = 3.916666667
0.5x + x2 = 3.916666667

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 = 3.916666667 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 3.916666667 + 0.0625

Combine like terms: 3.916666667 + 0.0625 = 3.979166667
0.0625 + 0.5x + x2 = 3.979166667

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 3.979166667

Calculate the square root of the right side: 1.994784867

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.994784867 and -1.994784867.

Subproblem 1
x + 0.25 = 1.994784867

Simplifying
x + 0.25 = 1.994784867

Reorder the terms:
0.25 + x = 1.994784867

Solving
0.25 + x = 1.994784867

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 = 1.994784867 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.994784867 + -0.25
x = 1.994784867 + -0.25

Combine like terms: 1.994784867 + -0.25 = 1.744784867
x = 1.744784867

Simplifying
x = 1.744784867

Subproblem 2
x + 0.25 = -1.994784867

Simplifying
x + 0.25 = -1.994784867

Reorder the terms:
0.25 + x = -1.994784867

Solving
0.25 + x = -1.994784867

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 = -1.994784867 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.994784867 + -0.25
x = -1.994784867 + -0.25

Combine like terms: -1.994784867 + -0.25 = -2.244784867
x = -2.244784867

Simplifying
x = -2.244784867

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.744784867, -2.244784867}