0.5(3x+5)0.1(12x-5)=3(1+0.1x)

Solution for 0.5(3x+5)0.1(12x-5)=3(1+0.1x) equation:

Simplifying
0.5(3x + 5) * 0.1(12x + -5) = 3(1 + 0.1x)

Reorder the terms:
0.5(5 + 3x) * 0.1(12x + -5) = 3(1 + 0.1x)

Reorder the terms:
0.5(5 + 3x) * 0.1(-5 + 12x) = 3(1 + 0.1x)

Reorder the terms for easier multiplication:
0.5 * 0.1(5 + 3x)(-5 + 12x) = 3(1 + 0.1x)

Multiply 0.5 * 0.1
0.05(5 + 3x)(-5 + 12x) = 3(1 + 0.1x)

Multiply (5 + 3x) * (-5 + 12x)
0.05(5(-5 + 12x) + 3x * (-5 + 12x)) = 3(1 + 0.1x)
0.05((-5 * 5 + 12x * 5) + 3x * (-5 + 12x)) = 3(1 + 0.1x)
0.05((-25 + 60x) + 3x * (-5 + 12x)) = 3(1 + 0.1x)
0.05(-25 + 60x + (-5 * 3x + 12x * 3x)) = 3(1 + 0.1x)
0.05(-25 + 60x + (-15x + 36x2)) = 3(1 + 0.1x)

Combine like terms: 60x + -15x = 45x
0.05(-25 + 45x + 36x2) = 3(1 + 0.1x)
(-25 * 0.05 + 45x * 0.05 + 36x2 * 0.05) = 3(1 + 0.1x)
(-1.25 + 2.25x + 1.8x2) = 3(1 + 0.1x)
-1.25 + 2.25x + 1.8x2 = (1 * 3 + 0.1x * 3)
-1.25 + 2.25x + 1.8x2 = (3 + 0.3x)

Solving
-1.25 + 2.25x + 1.8x2 = 3 + 0.3x

Solving for variable 'x'.

Reorder the terms:
-1.25 + -3 + 2.25x + -0.3x + 1.8x2 = 3 + 0.3x + -3 + -0.3x

Combine like terms: -1.25 + -3 = -4.25
-4.25 + 2.25x + -0.3x + 1.8x2 = 3 + 0.3x + -3 + -0.3x

Combine like terms: 2.25x + -0.3x = 1.95x
-4.25 + 1.95x + 1.8x2 = 3 + 0.3x + -3 + -0.3x

Reorder the terms:
-4.25 + 1.95x + 1.8x2 = 3 + -3 + 0.3x + -0.3x

Combine like terms: 3 + -3 = 0
-4.25 + 1.95x + 1.8x2 = 0 + 0.3x + -0.3x
-4.25 + 1.95x + 1.8x2 = 0.3x + -0.3x

Combine like terms: 0.3x + -0.3x = 0.0
-4.25 + 1.95x + 1.8x2 = 0.0

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

Divide each side by '1.8'.
-2.361111111 + 1.083333333x + x2 = 0

Move the constant term to the right:

Add '2.361111111' to each side of the equation.
-2.361111111 + 1.083333333x + 2.361111111 + x2 = 0 + 2.361111111

Reorder the terms:
-2.361111111 + 2.361111111 + 1.083333333x + x2 = 0 + 2.361111111

Combine like terms: -2.361111111 + 2.361111111 = 0.000000000
0.000000000 + 1.083333333x + x2 = 0 + 2.361111111
1.083333333x + x2 = 0 + 2.361111111

Combine like terms: 0 + 2.361111111 = 2.361111111
1.083333333x + x2 = 2.361111111

The x term is 1.083333333x.  Take half its coefficient (0.5416666665).
Square it (0.2934027776) and add it to both sides.

Add '0.2934027776' to each side of the equation.
1.083333333x + 0.2934027776 + x2 = 2.361111111 + 0.2934027776

Reorder the terms:
0.2934027776 + 1.083333333x + x2 = 2.361111111 + 0.2934027776

Combine like terms: 2.361111111 + 0.2934027776 = 2.6545138886
0.2934027776 + 1.083333333x + x2 = 2.6545138886

Factor a perfect square on the left side:
(x + 0.5416666665)(x + 0.5416666665) = 2.6545138886

Calculate the square root of the right side: 1.6292679

Break this problem into two subproblems by setting 
(x + 0.5416666665) equal to 1.6292679 and -1.6292679.

Subproblem 1
x + 0.5416666665 = 1.6292679

Simplifying
x + 0.5416666665 = 1.6292679

Reorder the terms:
0.5416666665 + x = 1.6292679

Solving
0.5416666665 + x = 1.6292679

Solving for variable 'x'.

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

Add '-0.5416666665' to each side of the equation.
0.5416666665 + -0.5416666665 + x = 1.6292679 + -0.5416666665

Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000
0.0000000000 + x = 1.6292679 + -0.5416666665
x = 1.6292679 + -0.5416666665

Combine like terms: 1.6292679 + -0.5416666665 = 1.0876012335
x = 1.0876012335

Simplifying
x = 1.0876012335

Subproblem 2
x + 0.5416666665 = -1.6292679

Simplifying
x + 0.5416666665 = -1.6292679

Reorder the terms:
0.5416666665 + x = -1.6292679

Solving
0.5416666665 + x = -1.6292679

Solving for variable 'x'.

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

Add '-0.5416666665' to each side of the equation.
0.5416666665 + -0.5416666665 + x = -1.6292679 + -0.5416666665

Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000
0.0000000000 + x = -1.6292679 + -0.5416666665
x = -1.6292679 + -0.5416666665

Combine like terms: -1.6292679 + -0.5416666665 = -2.1709345665
x = -2.1709345665

Simplifying
x = -2.1709345665

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0876012335, -2.1709345665}