30(8x+3)(8x+3)=300

Solution for 30(8x+3)(8x+3)=300 equation:

Simplifying
30(8x + 3)(8x + 3) = 300

Reorder the terms:
30(3 + 8x)(8x + 3) = 300

Reorder the terms:
30(3 + 8x)(3 + 8x) = 300

Multiply (3 + 8x) * (3 + 8x)
30(3(3 + 8x) + 8x * (3 + 8x)) = 300
30((3 * 3 + 8x * 3) + 8x * (3 + 8x)) = 300
30((9 + 24x) + 8x * (3 + 8x)) = 300
30(9 + 24x + (3 * 8x + 8x * 8x)) = 300
30(9 + 24x + (24x + 64x2)) = 300

Combine like terms: 24x + 24x = 48x
30(9 + 48x + 64x2) = 300
(9 * 30 + 48x * 30 + 64x2 * 30) = 300
(270 + 1440x + 1920x2) = 300

Solving
270 + 1440x + 1920x2 = 300

Solving for variable 'x'.

Reorder the terms:
270 + -300 + 1440x + 1920x2 = 300 + -300

Combine like terms: 270 + -300 = -30
-30 + 1440x + 1920x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-30 + 1440x + 1920x2 = 0

Factor out the Greatest Common Factor (GCF), '30'.
30(-1 + 48x + 64x2) = 0

Ignore the factor 30.
Subproblem 1
Set the factor '(-1 + 48x + 64x2)' equal to zero and attempt to solve:

Simplifying
-1 + 48x + 64x2 = 0

Solving
-1 + 48x + 64x2 = 0

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

Divide each side by '64'.
-0.015625 + 0.75x + x2 = 0

Move the constant term to the right:

Add '0.015625' to each side of the equation.
-0.015625 + 0.75x + 0.015625 + x2 = 0 + 0.015625

Reorder the terms:
-0.015625 + 0.015625 + 0.75x + x2 = 0 + 0.015625

Combine like terms: -0.015625 + 0.015625 = 0.000000
0.000000 + 0.75x + x2 = 0 + 0.015625
0.75x + x2 = 0 + 0.015625

Combine like terms: 0 + 0.015625 = 0.015625
0.75x + x2 = 0.015625

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 0.015625 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 0.015625 + 0.140625

Combine like terms: 0.015625 + 0.140625 = 0.15625
0.140625 + 0.75x + x2 = 0.15625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 0.15625

Calculate the square root of the right side: 0.395284708

Break this problem into two subproblems by setting 
(x + 0.375) equal to 0.395284708 and -0.395284708.

Subproblem 1
x + 0.375 = 0.395284708

Simplifying
x + 0.375 = 0.395284708

Reorder the terms:
0.375 + x = 0.395284708

Solving
0.375 + x = 0.395284708

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 0.395284708 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 0.395284708 + -0.375
x = 0.395284708 + -0.375

Combine like terms: 0.395284708 + -0.375 = 0.020284708
x = 0.020284708

Simplifying
x = 0.020284708

Subproblem 2
x + 0.375 = -0.395284708

Simplifying
x + 0.375 = -0.395284708

Reorder the terms:
0.375 + x = -0.395284708

Solving
0.375 + x = -0.395284708

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -0.395284708 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -0.395284708 + -0.375
x = -0.395284708 + -0.375

Combine like terms: -0.395284708 + -0.375 = -0.770284708
x = -0.770284708

Simplifying
x = -0.770284708

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.020284708, -0.770284708}
Solution
x = {0.020284708, -0.770284708}