4(x+5)(x-3)=40

Solution for 4(x+5)(x-3)=40 equation:

Simplifying
4(x + 5)(x + -3) = 40

Reorder the terms:
4(5 + x)(x + -3) = 40

Reorder the terms:
4(5 + x)(-3 + x) = 40

Multiply (5 + x) * (-3 + x)
4(5(-3 + x) + x(-3 + x)) = 40
4((-3 * 5 + x * 5) + x(-3 + x)) = 40
4((-15 + 5x) + x(-3 + x)) = 40
4(-15 + 5x + (-3 * x + x * x)) = 40
4(-15 + 5x + (-3x + x2)) = 40

Combine like terms: 5x + -3x = 2x
4(-15 + 2x + x2) = 40
(-15 * 4 + 2x * 4 + x2 * 4) = 40
(-60 + 8x + 4x2) = 40

Solving
-60 + 8x + 4x2 = 40

Solving for variable 'x'.

Reorder the terms:
-60 + -40 + 8x + 4x2 = 40 + -40

Combine like terms: -60 + -40 = -100
-100 + 8x + 4x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-100 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + 2x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-25 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-25 + 2x + x2 = 0

Solving
-25 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 2x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 2x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 2x + x2 = 0 + 25
2x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
2x + x2 = 25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 25 + 1

Reorder the terms:
1 + 2x + x2 = 25 + 1

Combine like terms: 25 + 1 = 26
1 + 2x + x2 = 26

Factor a perfect square on the left side:
(x + 1)(x + 1) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + 1) equal to 5.099019514 and -5.099019514.

Subproblem 1
x + 1 = 5.099019514

Simplifying
x + 1 = 5.099019514

Reorder the terms:
1 + x = 5.099019514

Solving
1 + x = 5.099019514

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.099019514 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.099019514 + -1
x = 5.099019514 + -1

Combine like terms: 5.099019514 + -1 = 4.099019514
x = 4.099019514

Simplifying
x = 4.099019514

Subproblem 2
x + 1 = -5.099019514

Simplifying
x + 1 = -5.099019514

Reorder the terms:
1 + x = -5.099019514

Solving
1 + x = -5.099019514

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.099019514 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.099019514 + -1
x = -5.099019514 + -1

Combine like terms: -5.099019514 + -1 = -6.099019514
x = -6.099019514

Simplifying
x = -6.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.099019514, -6.099019514}
Solution
x = {4.099019514, -6.099019514}