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

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

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

Reorder the terms:
4x(-5 + x) = 3(x + 5)
(-5 * 4x + x * 4x) = 3(x + 5)
(-20x + 4x2) = 3(x + 5)

Reorder the terms:
-20x + 4x2 = 3(5 + x)
-20x + 4x2 = (5 * 3 + x * 3)
-20x + 4x2 = (15 + 3x)

Solving
-20x + 4x2 = 15 + 3x

Solving for variable 'x'.

Reorder the terms:
-15 + -20x + -3x + 4x2 = 15 + 3x + -15 + -3x

Combine like terms: -20x + -3x = -23x
-15 + -23x + 4x2 = 15 + 3x + -15 + -3x

Reorder the terms:
-15 + -23x + 4x2 = 15 + -15 + 3x + -3x

Combine like terms: 15 + -15 = 0
-15 + -23x + 4x2 = 0 + 3x + -3x
-15 + -23x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-15 + -23x + 4x2 = 0

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

Divide each side by '4'.
-3.75 + -5.75x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -5.75x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -5.75x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -5.75x + x2 = 0 + 3.75
-5.75x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-5.75x + x2 = 3.75

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = 3.75 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = 3.75 + 8.265625

Combine like terms: 3.75 + 8.265625 = 12.015625
8.265625 + -5.75x + x2 = 12.015625

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = 12.015625

Calculate the square root of the right side: 3.466356156

Break this problem into two subproblems by setting 
(x + -2.875) equal to 3.466356156 and -3.466356156.

Subproblem 1
x + -2.875 = 3.466356156

Simplifying
x + -2.875 = 3.466356156

Reorder the terms:
-2.875 + x = 3.466356156

Solving
-2.875 + x = 3.466356156

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = 3.466356156 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = 3.466356156 + 2.875
x = 3.466356156 + 2.875

Combine like terms: 3.466356156 + 2.875 = 6.341356156
x = 6.341356156

Simplifying
x = 6.341356156

Subproblem 2
x + -2.875 = -3.466356156

Simplifying
x + -2.875 = -3.466356156

Reorder the terms:
-2.875 + x = -3.466356156

Solving
-2.875 + x = -3.466356156

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = -3.466356156 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = -3.466356156 + 2.875
x = -3.466356156 + 2.875

Combine like terms: -3.466356156 + 2.875 = -0.591356156
x = -0.591356156

Simplifying
x = -0.591356156

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.341356156, -0.591356156}