15x^2+12x-60=0

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Solution for 15x^2+12x-60=0 equation: 


Simplifying
15x2 + 12x + -60 = 0

Reorder the terms:
-60 + 12x + 15x2 = 0

Solving
-60 + 12x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + 4x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-20 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
-20 + 4x + 5x2 = 0

Solving
-20 + 4x + 5x2 = 0

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

Divide each side by '5'.
-4 + 0.8x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.8x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.8x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.8x + x2 = 0 + 4
0.8x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.8x + x2 = 4

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 = 4 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 4 + 0.16

Combine like terms: 4 + 0.16 = 4.16
0.16 + 0.8x + x2 = 4.16

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 4.16

Calculate the square root of the right side: 2.039607805

Break this problem into two subproblems by setting 
(x + 0.4) equal to 2.039607805 and -2.039607805.


Subproblem 1
x + 0.4 = 2.039607805

Simplifying
x + 0.4 = 2.039607805

Reorder the terms:
0.4 + x = 2.039607805

Solving
0.4 + x = 2.039607805

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 = 2.039607805 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 2.039607805 + -0.4
x = 2.039607805 + -0.4

Combine like terms: 2.039607805 + -0.4 = 1.639607805
x = 1.639607805

Simplifying
x = 1.639607805


Subproblem 2
x + 0.4 = -2.039607805

Simplifying
x + 0.4 = -2.039607805

Reorder the terms:
0.4 + x = -2.039607805

Solving
0.4 + x = -2.039607805

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 = -2.039607805 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -2.039607805 + -0.4
x = -2.039607805 + -0.4

Combine like terms: -2.039607805 + -0.4 = -2.439607805
x = -2.439607805

Simplifying
x = -2.439607805


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.639607805, -2.439607805}
Solution
x = {1.639607805, -2.439607805}

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