3x(8x+15)=180

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Solution for 3x(8x+15)=180 equation: 


Simplifying
3x(8x + 15) = 180

Reorder the terms:
3x(15 + 8x) = 180
(15 * 3x + 8x * 3x) = 180
(45x + 24x2) = 180

Solving
45x + 24x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 45x + 24x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 45x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 15x + 8x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + 15x + 8x2)' equal to zero and attempt to solve:

Simplifying
-60 + 15x + 8x2 = 0

Solving
-60 + 15x + 8x2 = 0

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

Divide each side by '8'.
-7.5 + 1.875x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 1.875x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 1.875x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 1.875x + x2 = 0 + 7.5
1.875x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
1.875x + x2 = 7.5

The x term is 1.875x.  Take half its coefficient (0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
1.875x + 0.87890625 + x2 = 7.5 + 0.87890625

Reorder the terms:
0.87890625 + 1.875x + x2 = 7.5 + 0.87890625

Combine like terms: 7.5 + 0.87890625 = 8.37890625
0.87890625 + 1.875x + x2 = 8.37890625

Factor a perfect square on the left side:
(x + 0.9375)(x + 0.9375) = 8.37890625

Calculate the square root of the right side: 2.894634044

Break this problem into two subproblems by setting 
(x + 0.9375) equal to 2.894634044 and -2.894634044.


Subproblem 1
x + 0.9375 = 2.894634044

Simplifying
x + 0.9375 = 2.894634044

Reorder the terms:
0.9375 + x = 2.894634044

Solving
0.9375 + x = 2.894634044

Solving for variable 'x'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + x = 2.894634044 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + x = 2.894634044 + -0.9375
x = 2.894634044 + -0.9375

Combine like terms: 2.894634044 + -0.9375 = 1.957134044
x = 1.957134044

Simplifying
x = 1.957134044


Subproblem 2
x + 0.9375 = -2.894634044

Simplifying
x + 0.9375 = -2.894634044

Reorder the terms:
0.9375 + x = -2.894634044

Solving
0.9375 + x = -2.894634044

Solving for variable 'x'.

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

Add '-0.9375' to each side of the equation.
0.9375 + -0.9375 + x = -2.894634044 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + x = -2.894634044 + -0.9375
x = -2.894634044 + -0.9375

Combine like terms: -2.894634044 + -0.9375 = -3.832134044
x = -3.832134044

Simplifying
x = -3.832134044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.957134044, -3.832134044}
Solution
x = {1.957134044, -3.832134044}

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