6(5x+6)3x+3=103

Solution for 6(5x+6)3x+3=103 equation:

Simplifying
6(5x + 6) * 3x + 3 = 103

Reorder the terms:
6(6 + 5x) * 3x + 3 = 103

Reorder the terms for easier multiplication:
6 * 3x(6 + 5x) + 3 = 103

Multiply 6 * 3
18x(6 + 5x) + 3 = 103
(6 * 18x + 5x * 18x) + 3 = 103
(108x + 90x2) + 3 = 103

Reorder the terms:
3 + 108x + 90x2 = 103

Solving
3 + 108x + 90x2 = 103

Solving for variable 'x'.

Reorder the terms:
3 + -103 + 108x + 90x2 = 103 + -103

Combine like terms: 3 + -103 = -100
-100 + 108x + 90x2 = 103 + -103

Combine like terms: 103 + -103 = 0
-100 + 108x + 90x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 54x + 45x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + 54x + 45x2)' equal to zero and attempt to solve:

Simplifying
-50 + 54x + 45x2 = 0

Solving
-50 + 54x + 45x2 = 0

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

Divide each side by '45'.
-1.111111111 + 1.2x + x2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 1.2x + 1.111111111 + x2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 1.2x + x2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 1.2x + x2 = 0 + 1.111111111
1.2x + x2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
1.2x + x2 = 1.111111111

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 1.111111111 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 1.111111111 + 0.36

Combine like terms: 1.111111111 + 0.36 = 1.471111111
0.36 + 1.2x + x2 = 1.471111111

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 1.471111111

Calculate the square root of the right side: 1.212893693

Break this problem into two subproblems by setting 
(x + 0.6) equal to 1.212893693 and -1.212893693.

Subproblem 1
x + 0.6 = 1.212893693

Simplifying
x + 0.6 = 1.212893693

Reorder the terms:
0.6 + x = 1.212893693

Solving
0.6 + x = 1.212893693

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = 1.212893693 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = 1.212893693 + -0.6
x = 1.212893693 + -0.6

Combine like terms: 1.212893693 + -0.6 = 0.612893693
x = 0.612893693

Simplifying
x = 0.612893693

Subproblem 2
x + 0.6 = -1.212893693

Simplifying
x + 0.6 = -1.212893693

Reorder the terms:
0.6 + x = -1.212893693

Solving
0.6 + x = -1.212893693

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = -1.212893693 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = -1.212893693 + -0.6
x = -1.212893693 + -0.6

Combine like terms: -1.212893693 + -0.6 = -1.812893693
x = -1.812893693

Simplifying
x = -1.812893693

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.612893693, -1.812893693}
Solution
x = {0.612893693, -1.812893693}