2x(3x+5)=60

Solution for 2x(3x+5)=60 equation:

Simplifying
2x(3x + 5) = 60

Reorder the terms:
2x(5 + 3x) = 60
(5 * 2x + 3x * 2x) = 60
(10x + 6x2) = 60

Solving
10x + 6x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + 10x + 6x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 5x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-30 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-30 + 5x + 3x2 = 0

Solving
-30 + 5x + 3x2 = 0

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

Divide each side by '3'.
-10 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 1.666666667x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 1.666666667x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 1.666666667x + x2 = 0 + 10
1.666666667x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
1.666666667x + x2 = 10

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 10 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 10 + 0.6944444447

Combine like terms: 10 + 0.6944444447 = 10.6944444447
0.6944444447 + 1.666666667x + x2 = 10.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 10.6944444447

Calculate the square root of the right side: 3.270236145

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 3.270236145 and -3.270236145.

Subproblem 1
x + 0.8333333335 = 3.270236145

Simplifying
x + 0.8333333335 = 3.270236145

Reorder the terms:
0.8333333335 + x = 3.270236145

Solving
0.8333333335 + x = 3.270236145

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 3.270236145 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 3.270236145 + -0.8333333335
x = 3.270236145 + -0.8333333335

Combine like terms: 3.270236145 + -0.8333333335 = 2.4369028115
x = 2.4369028115

Simplifying
x = 2.4369028115

Subproblem 2
x + 0.8333333335 = -3.270236145

Simplifying
x + 0.8333333335 = -3.270236145

Reorder the terms:
0.8333333335 + x = -3.270236145

Solving
0.8333333335 + x = -3.270236145

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -3.270236145 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -3.270236145 + -0.8333333335
x = -3.270236145 + -0.8333333335

Combine like terms: -3.270236145 + -0.8333333335 = -4.1035694785
x = -4.1035694785

Simplifying
x = -4.1035694785

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.4369028115, -4.1035694785}
Solution
x = {2.4369028115, -4.1035694785}