3x^2-15x-153=0

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Solution for 3x^2-15x-153=0 equation: 


Simplifying
3x2 + -15x + -153 = 0

Reorder the terms:
-153 + -15x + 3x2 = 0

Solving
-153 + -15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-51 + -5x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-51 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-51 + -5x + x2 = 0

Solving
-51 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -5x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + -5x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -5x + x2 = 0 + 51
-5x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
-5x + x2 = 51

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 51 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 51 + 6.25

Combine like terms: 51 + 6.25 = 57.25
6.25 + -5x + x2 = 57.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(x + -2.5) equal to 7.566372975 and -7.566372975.


Subproblem 1
x + -2.5 = 7.566372975

Simplifying
x + -2.5 = 7.566372975

Reorder the terms:
-2.5 + x = 7.566372975

Solving
-2.5 + x = 7.566372975

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 7.566372975 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 7.566372975 + 2.5
x = 7.566372975 + 2.5

Combine like terms: 7.566372975 + 2.5 = 10.066372975
x = 10.066372975

Simplifying
x = 10.066372975


Subproblem 2
x + -2.5 = -7.566372975

Simplifying
x + -2.5 = -7.566372975

Reorder the terms:
-2.5 + x = -7.566372975

Solving
-2.5 + x = -7.566372975

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -7.566372975 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -7.566372975 + 2.5
x = -7.566372975 + 2.5

Combine like terms: -7.566372975 + 2.5 = -5.066372975
x = -5.066372975

Simplifying
x = -5.066372975


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.066372975, -5.066372975}
Solution
x = {10.066372975, -5.066372975}

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