3x^2+84x+153=0

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Solution for 3x^2+84x+153=0 equation: 


Simplifying
3x2 + 84x + 153 = 0

Reorder the terms:
153 + 84x + 3x2 = 0

Solving
153 + 84x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(51 + 28x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(51 + 28x + x2)' equal to zero and attempt to solve:

Simplifying
51 + 28x + x2 = 0

Solving
51 + 28x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-51' to each side of the equation.
51 + 28x + -51 + x2 = 0 + -51

Reorder the terms:
51 + -51 + 28x + x2 = 0 + -51

Combine like terms: 51 + -51 = 0
0 + 28x + x2 = 0 + -51
28x + x2 = 0 + -51

Combine like terms: 0 + -51 = -51
28x + x2 = -51

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = -51 + 196

Reorder the terms:
196 + 28x + x2 = -51 + 196

Combine like terms: -51 + 196 = 145
196 + 28x + x2 = 145

Factor a perfect square on the left side:
(x + 14)(x + 14) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(x + 14) equal to 12.041594579 and -12.041594579.


Subproblem 1
x + 14 = 12.041594579

Simplifying
x + 14 = 12.041594579

Reorder the terms:
14 + x = 12.041594579

Solving
14 + x = 12.041594579

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = 12.041594579 + -14

Combine like terms: 14 + -14 = 0
0 + x = 12.041594579 + -14
x = 12.041594579 + -14

Combine like terms: 12.041594579 + -14 = -1.958405421
x = -1.958405421

Simplifying
x = -1.958405421


Subproblem 2
x + 14 = -12.041594579

Simplifying
x + 14 = -12.041594579

Reorder the terms:
14 + x = -12.041594579

Solving
14 + x = -12.041594579

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = -12.041594579 + -14

Combine like terms: 14 + -14 = 0
0 + x = -12.041594579 + -14
x = -12.041594579 + -14

Combine like terms: -12.041594579 + -14 = -26.041594579
x = -26.041594579

Simplifying
x = -26.041594579


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.958405421, -26.041594579}
Solution
x = {-1.958405421, -26.041594579}

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