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

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


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

Remove parenthesis around (3x)
3x(5x + 4) = 24

Reorder the terms:
3x(4 + 5x) = 24
(4 * 3x + 5x * 3x) = 24
(12x + 15x2) = 24

Solving
12x + 15x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 12x + 15x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 12x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 4x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
-8 + 4x + 5x2 = 0

Solving
-8 + 4x + 5x2 = 0

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

Divide each side by '5'.
-1.6 + 0.8x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.8x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.8x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.8x + x2 = 0 + 1.6
0.8x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.8x + x2 = 1.6

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 1.6 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 1.6 + 0.16

Combine like terms: 1.6 + 0.16 = 1.76
0.16 + 0.8x + x2 = 1.76

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 1.76

Calculate the square root of the right side: 1.326649916

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.326649916 and -1.326649916.


Subproblem 1
x + 0.4 = 1.326649916

Simplifying
x + 0.4 = 1.326649916

Reorder the terms:
0.4 + x = 1.326649916

Solving
0.4 + x = 1.326649916

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 1.326649916 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 1.326649916 + -0.4
x = 1.326649916 + -0.4

Combine like terms: 1.326649916 + -0.4 = 0.926649916
x = 0.926649916

Simplifying
x = 0.926649916


Subproblem 2
x + 0.4 = -1.326649916

Simplifying
x + 0.4 = -1.326649916

Reorder the terms:
0.4 + x = -1.326649916

Solving
0.4 + x = -1.326649916

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -1.326649916 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -1.326649916 + -0.4
x = -1.326649916 + -0.4

Combine like terms: -1.326649916 + -0.4 = -1.726649916
x = -1.726649916

Simplifying
x = -1.726649916


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.926649916, -1.726649916}
Solution
x = {0.926649916, -1.726649916}

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