7x(15x+24)=6(500-12x)

Solution for 7x(15x+24)=6(500-12x) equation:

Simplifying
7x(15x + 24) = 6(500 + -12x)

Reorder the terms:
7x(24 + 15x) = 6(500 + -12x)
(24 * 7x + 15x * 7x) = 6(500 + -12x)
(168x + 105x2) = 6(500 + -12x)
168x + 105x2 = (500 * 6 + -12x * 6)
168x + 105x2 = (3000 + -72x)

Solving
168x + 105x2 = 3000 + -72x

Solving for variable 'x'.

Reorder the terms:
-3000 + 168x + 72x + 105x2 = 3000 + -72x + -3000 + 72x

Combine like terms: 168x + 72x = 240x
-3000 + 240x + 105x2 = 3000 + -72x + -3000 + 72x

Reorder the terms:
-3000 + 240x + 105x2 = 3000 + -3000 + -72x + 72x

Combine like terms: 3000 + -3000 = 0
-3000 + 240x + 105x2 = 0 + -72x + 72x
-3000 + 240x + 105x2 = -72x + 72x

Combine like terms: -72x + 72x = 0
-3000 + 240x + 105x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-200 + 16x + 7x2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-200 + 16x + 7x2)' equal to zero and attempt to solve:

Simplifying
-200 + 16x + 7x2 = 0

Solving
-200 + 16x + 7x2 = 0

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

Divide each side by '7'.
-28.57142857 + 2.285714286x + x2 = 0

Move the constant term to the right:

Add '28.57142857' to each side of the equation.
-28.57142857 + 2.285714286x + 28.57142857 + x2 = 0 + 28.57142857

Reorder the terms:
-28.57142857 + 28.57142857 + 2.285714286x + x2 = 0 + 28.57142857

Combine like terms: -28.57142857 + 28.57142857 = 0.00000000
0.00000000 + 2.285714286x + x2 = 0 + 28.57142857
2.285714286x + x2 = 0 + 28.57142857

Combine like terms: 0 + 28.57142857 = 28.57142857
2.285714286x + x2 = 28.57142857

The x term is 2.285714286x.  Take half its coefficient (1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
2.285714286x + 1.306122449 + x2 = 28.57142857 + 1.306122449

Reorder the terms:
1.306122449 + 2.285714286x + x2 = 28.57142857 + 1.306122449

Combine like terms: 28.57142857 + 1.306122449 = 29.877551019
1.306122449 + 2.285714286x + x2 = 29.877551019

Factor a perfect square on the left side:
(x + 1.142857143)(x + 1.142857143) = 29.877551019

Calculate the square root of the right side: 5.466036134

Break this problem into two subproblems by setting 
(x + 1.142857143) equal to 5.466036134 and -5.466036134.

Subproblem 1
x + 1.142857143 = 5.466036134

Simplifying
x + 1.142857143 = 5.466036134

Reorder the terms:
1.142857143 + x = 5.466036134

Solving
1.142857143 + x = 5.466036134

Solving for variable 'x'.

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

Add '-1.142857143' to each side of the equation.
1.142857143 + -1.142857143 + x = 5.466036134 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + x = 5.466036134 + -1.142857143
x = 5.466036134 + -1.142857143

Combine like terms: 5.466036134 + -1.142857143 = 4.323178991
x = 4.323178991

Simplifying
x = 4.323178991

Subproblem 2
x + 1.142857143 = -5.466036134

Simplifying
x + 1.142857143 = -5.466036134

Reorder the terms:
1.142857143 + x = -5.466036134

Solving
1.142857143 + x = -5.466036134

Solving for variable 'x'.

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

Add '-1.142857143' to each side of the equation.
1.142857143 + -1.142857143 + x = -5.466036134 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + x = -5.466036134 + -1.142857143
x = -5.466036134 + -1.142857143

Combine like terms: -5.466036134 + -1.142857143 = -6.608893277
x = -6.608893277

Simplifying
x = -6.608893277

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.323178991, -6.608893277}
Solution
x = {4.323178991, -6.608893277}