60=(2x+3)(2x)

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

Simplifying
60 = (2x + 3)(2x)

Reorder the terms:
60 = (3 + 2x)(2x)

Remove parenthesis around (2x)
60 = (3 + 2x) * 2x

Reorder the terms for easier multiplication:
60 = 2x(3 + 2x)
60 = (3 * 2x + 2x * 2x)
60 = (6x + 4x2)

Solving
60 = 6x + 4x2

Solving for variable 'x'.

Reorder the terms:
60 + -6x + -4x2 = 6x + -6x + 4x2 + -4x2

Combine like terms: 6x + -6x = 0
60 + -6x + -4x2 = 0 + 4x2 + -4x2
60 + -6x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
60 + -6x + -4x2 = 0

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

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

Simplifying
30 + -3x + -2x2 = 0

Solving
30 + -3x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-15 + 1.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 1.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 1.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 1.5x + x2 = 0 + 15
1.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
1.5x + x2 = 15

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 15 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 15 + 0.5625

Combine like terms: 15 + 0.5625 = 15.5625
0.5625 + 1.5x + x2 = 15.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(x + 0.75) equal to 3.94493346 and -3.94493346.

Subproblem 1
x + 0.75 = 3.94493346

Simplifying
x + 0.75 = 3.94493346

Reorder the terms:
0.75 + x = 3.94493346

Solving
0.75 + x = 3.94493346

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 3.94493346 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 3.94493346 + -0.75
x = 3.94493346 + -0.75

Combine like terms: 3.94493346 + -0.75 = 3.19493346
x = 3.19493346

Simplifying
x = 3.19493346

Subproblem 2
x + 0.75 = -3.94493346

Simplifying
x + 0.75 = -3.94493346

Reorder the terms:
0.75 + x = -3.94493346

Solving
0.75 + x = -3.94493346

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -3.94493346 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -3.94493346 + -0.75
x = -3.94493346 + -0.75

Combine like terms: -3.94493346 + -0.75 = -4.69493346
x = -4.69493346

Simplifying
x = -4.69493346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.19493346, -4.69493346}
Solution
x = {3.19493346, -4.69493346}