0.04x(x-12)+0.06x=1.52

Solution for 0.04x(x-12)+0.06x=1.52 equation:

Simplifying
0.04x(x + -12) + 0.06x = 1.52

Reorder the terms:
0.04x(-12 + x) + 0.06x = 1.52
(-12 * 0.04x + x * 0.04x) + 0.06x = 1.52
(-0.48x + 0.04x2) + 0.06x = 1.52

Reorder the terms:
-0.48x + 0.06x + 0.04x2 = 1.52

Combine like terms: -0.48x + 0.06x = -0.42x
-0.42x + 0.04x2 = 1.52

Solving
-0.42x + 0.04x2 = 1.52

Solving for variable 'x'.

Reorder the terms:
-1.52 + -0.42x + 0.04x2 = 1.52 + -1.52

Combine like terms: 1.52 + -1.52 = 0.00
-1.52 + -0.42x + 0.04x2 = 0.00

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

Divide each side by '0.04'.
-38 + -10.5x + x2 = 0

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -10.5x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + -10.5x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -10.5x + x2 = 0 + 38
-10.5x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
-10.5x + x2 = 38

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = 38 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = 38 + 27.5625

Combine like terms: 38 + 27.5625 = 65.5625
27.5625 + -10.5x + x2 = 65.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 65.5625

Calculate the square root of the right side: 8.09706737

Break this problem into two subproblems by setting 
(x + -5.25) equal to 8.09706737 and -8.09706737.

Subproblem 1
x + -5.25 = 8.09706737

Simplifying
x + -5.25 = 8.09706737

Reorder the terms:
-5.25 + x = 8.09706737

Solving
-5.25 + x = 8.09706737

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = 8.09706737 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = 8.09706737 + 5.25
x = 8.09706737 + 5.25

Combine like terms: 8.09706737 + 5.25 = 13.34706737
x = 13.34706737

Simplifying
x = 13.34706737

Subproblem 2
x + -5.25 = -8.09706737

Simplifying
x + -5.25 = -8.09706737

Reorder the terms:
-5.25 + x = -8.09706737

Solving
-5.25 + x = -8.09706737

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = -8.09706737 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = -8.09706737 + 5.25
x = -8.09706737 + 5.25

Combine like terms: -8.09706737 + 5.25 = -2.84706737
x = -2.84706737

Simplifying
x = -2.84706737

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.34706737, -2.84706737}