4x(x-3)=25

Solution for 4x(x-3)=25 equation:

Simplifying
4x(x + -3) = 25

Reorder the terms:
4x(-3 + x) = 25
(-3 * 4x + x * 4x) = 25
(-12x + 4x2) = 25

Solving
-12x + 4x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + -12x + 4x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -12x + 4x2 = 0

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

Divide each side by '4'.
-6.25 + -3x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -3x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -3x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -3x + x2 = 0 + 6.25
-3x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-3x + x2 = 6.25

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 6.25 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 6.25 + 2.25

Combine like terms: 6.25 + 2.25 = 8.5
2.25 + -3x + x2 = 8.5

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.915475947 and -2.915475947.

Subproblem 1
x + -1.5 = 2.915475947

Simplifying
x + -1.5 = 2.915475947

Reorder the terms:
-1.5 + x = 2.915475947

Solving
-1.5 + x = 2.915475947

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.915475947 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.915475947 + 1.5
x = 2.915475947 + 1.5

Combine like terms: 2.915475947 + 1.5 = 4.415475947
x = 4.415475947

Simplifying
x = 4.415475947

Subproblem 2
x + -1.5 = -2.915475947

Simplifying
x + -1.5 = -2.915475947

Reorder the terms:
-1.5 + x = -2.915475947

Solving
-1.5 + x = -2.915475947

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.915475947 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.915475947 + 1.5
x = -2.915475947 + 1.5

Combine like terms: -2.915475947 + 1.5 = -1.415475947
x = -1.415475947

Simplifying
x = -1.415475947

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.415475947, -1.415475947}