24=3x(4*5+x)

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Solution for 24=3x(4*5+x) equation: 


Simplifying
24 = 3x(4 * 5 + x)

Multiply 4 * 5
24 = 3x(20 + x)
24 = (20 * 3x + x * 3x)
24 = (60x + 3x2)

Solving
24 = 60x + 3x2

Solving for variable 'x'.

Reorder the terms:
24 + -60x + -3x2 = 60x + -60x + 3x2 + -3x2

Combine like terms: 60x + -60x = 0
24 + -60x + -3x2 = 0 + 3x2 + -3x2
24 + -60x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
24 + -60x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -20x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + -20x + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -20x + -1x2 = 0

Solving
8 + -20x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8 + 20x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 20x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 20x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 20x + x2 = 0 + 8
20x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
20x + x2 = 8

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 8 + 100

Reorder the terms:
100 + 20x + x2 = 8 + 100

Combine like terms: 8 + 100 = 108
100 + 20x + x2 = 108

Factor a perfect square on the left side:
(x + 10)(x + 10) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(x + 10) equal to 10.392304845 and -10.392304845.


Subproblem 1
x + 10 = 10.392304845

Simplifying
x + 10 = 10.392304845

Reorder the terms:
10 + x = 10.392304845

Solving
10 + x = 10.392304845

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 10.392304845 + -10

Combine like terms: 10 + -10 = 0
0 + x = 10.392304845 + -10
x = 10.392304845 + -10

Combine like terms: 10.392304845 + -10 = 0.392304845
x = 0.392304845

Simplifying
x = 0.392304845


Subproblem 2
x + 10 = -10.392304845

Simplifying
x + 10 = -10.392304845

Reorder the terms:
10 + x = -10.392304845

Solving
10 + x = -10.392304845

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -10.392304845 + -10

Combine like terms: 10 + -10 = 0
0 + x = -10.392304845 + -10
x = -10.392304845 + -10

Combine like terms: -10.392304845 + -10 = -20.392304845
x = -20.392304845

Simplifying
x = -20.392304845


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.392304845, -20.392304845}
Solution
x = {0.392304845, -20.392304845}

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