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

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

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

Reorder the terms:
5x(-5 + x) = (3x + 4)(x + 5)
(-5 * 5x + x * 5x) = (3x + 4)(x + 5)
(-25x + 5x2) = (3x + 4)(x + 5)

Reorder the terms:
-25x + 5x2 = (4 + 3x)(x + 5)

Reorder the terms:
-25x + 5x2 = (4 + 3x)(5 + x)

Multiply (4 + 3x) * (5 + x)
-25x + 5x2 = (4(5 + x) + 3x * (5 + x))
-25x + 5x2 = ((5 * 4 + x * 4) + 3x * (5 + x))
-25x + 5x2 = ((20 + 4x) + 3x * (5 + x))
-25x + 5x2 = (20 + 4x + (5 * 3x + x * 3x))
-25x + 5x2 = (20 + 4x + (15x + 3x2))

Combine like terms: 4x + 15x = 19x
-25x + 5x2 = (20 + 19x + 3x2)

Solving
-25x + 5x2 = 20 + 19x + 3x2

Solving for variable 'x'.

Reorder the terms:
-20 + -25x + -19x + 5x2 + -3x2 = 20 + 19x + 3x2 + -20 + -19x + -3x2

Combine like terms: -25x + -19x = -44x
-20 + -44x + 5x2 + -3x2 = 20 + 19x + 3x2 + -20 + -19x + -3x2

Combine like terms: 5x2 + -3x2 = 2x2
-20 + -44x + 2x2 = 20 + 19x + 3x2 + -20 + -19x + -3x2

Reorder the terms:
-20 + -44x + 2x2 = 20 + -20 + 19x + -19x + 3x2 + -3x2

Combine like terms: 20 + -20 = 0
-20 + -44x + 2x2 = 0 + 19x + -19x + 3x2 + -3x2
-20 + -44x + 2x2 = 19x + -19x + 3x2 + -3x2

Combine like terms: 19x + -19x = 0
-20 + -44x + 2x2 = 0 + 3x2 + -3x2
-20 + -44x + 2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-20 + -44x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -22x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -22x + x2)' equal to zero and attempt to solve:

Simplifying
-10 + -22x + x2 = 0

Solving
-10 + -22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -22x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -22x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -22x + x2 = 0 + 10
-22x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-22x + x2 = 10

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 10 + 121

Reorder the terms:
121 + -22x + x2 = 10 + 121

Combine like terms: 10 + 121 = 131
121 + -22x + x2 = 131

Factor a perfect square on the left side:
(x + -11)(x + -11) = 131

Calculate the square root of the right side: 11.445523142

Break this problem into two subproblems by setting 
(x + -11) equal to 11.445523142 and -11.445523142.

Subproblem 1
x + -11 = 11.445523142

Simplifying
x + -11 = 11.445523142

Reorder the terms:
-11 + x = 11.445523142

Solving
-11 + x = 11.445523142

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 11.445523142 + 11

Combine like terms: -11 + 11 = 0
0 + x = 11.445523142 + 11
x = 11.445523142 + 11

Combine like terms: 11.445523142 + 11 = 22.445523142
x = 22.445523142

Simplifying
x = 22.445523142

Subproblem 2
x + -11 = -11.445523142

Simplifying
x + -11 = -11.445523142

Reorder the terms:
-11 + x = -11.445523142

Solving
-11 + x = -11.445523142

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -11.445523142 + 11

Combine like terms: -11 + 11 = 0
0 + x = -11.445523142 + 11
x = -11.445523142 + 11

Combine like terms: -11.445523142 + 11 = -0.445523142
x = -0.445523142

Simplifying
x = -0.445523142

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.445523142, -0.445523142}
Solution
x = {22.445523142, -0.445523142}