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

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

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

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

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

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

Combine like terms: -5x + 8x = 3x
(-20 + 3x + 2x2) = -2(x + 3)

Reorder the terms:
-20 + 3x + 2x2 = -2(3 + x)
-20 + 3x + 2x2 = (3 * -2 + x * -2)
-20 + 3x + 2x2 = (-6 + -2x)

Solving
-20 + 3x + 2x2 = -6 + -2x

Solving for variable 'x'.

Reorder the terms:
-20 + 6 + 3x + 2x + 2x2 = -6 + -2x + 6 + 2x

Combine like terms: -20 + 6 = -14
-14 + 3x + 2x + 2x2 = -6 + -2x + 6 + 2x

Combine like terms: 3x + 2x = 5x
-14 + 5x + 2x2 = -6 + -2x + 6 + 2x

Reorder the terms:
-14 + 5x + 2x2 = -6 + 6 + -2x + 2x

Combine like terms: -6 + 6 = 0
-14 + 5x + 2x2 = 0 + -2x + 2x
-14 + 5x + 2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-14 + 5x + 2x2 = 0

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

Divide each side by '2'.
-7 + 2.5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 2.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 2.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2.5x + x2 = 0 + 7
2.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
2.5x + x2 = 7

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 7 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 7 + 1.5625

Combine like terms: 7 + 1.5625 = 8.5625
1.5625 + 2.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.926174978 and -2.926174978.

Subproblem 1
x + 1.25 = 2.926174978

Simplifying
x + 1.25 = 2.926174978

Reorder the terms:
1.25 + x = 2.926174978

Solving
1.25 + x = 2.926174978

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 2.926174978 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.926174978 + -1.25
x = 2.926174978 + -1.25

Combine like terms: 2.926174978 + -1.25 = 1.676174978
x = 1.676174978

Simplifying
x = 1.676174978

Subproblem 2
x + 1.25 = -2.926174978

Simplifying
x + 1.25 = -2.926174978

Reorder the terms:
1.25 + x = -2.926174978

Solving
1.25 + x = -2.926174978

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -2.926174978 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.926174978 + -1.25
x = -2.926174978 + -1.25

Combine like terms: -2.926174978 + -1.25 = -4.176174978
x = -4.176174978

Simplifying
x = -4.176174978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.676174978, -4.176174978}