-3x^2+42x+135=0

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Solution for -3x^2+42x+135=0 equation: 


Simplifying
-3x2 + 42x + 135 = 0

Reorder the terms:
135 + 42x + -3x2 = 0

Solving
135 + 42x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(45 + 14x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(45 + 14x + -1x2)' equal to zero and attempt to solve:

Simplifying
45 + 14x + -1x2 = 0

Solving
45 + 14x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-45 + -14x + x2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -14x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + -14x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -14x + x2 = 0 + 45
-14x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-14x + x2 = 45

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 45 + 49

Reorder the terms:
49 + -14x + x2 = 45 + 49

Combine like terms: 45 + 49 = 94
49 + -14x + x2 = 94

Factor a perfect square on the left side:
(x + -7)(x + -7) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(x + -7) equal to 9.695359715 and -9.695359715.


Subproblem 1
x + -7 = 9.695359715

Simplifying
x + -7 = 9.695359715

Reorder the terms:
-7 + x = 9.695359715

Solving
-7 + x = 9.695359715

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 9.695359715 + 7

Combine like terms: -7 + 7 = 0
0 + x = 9.695359715 + 7
x = 9.695359715 + 7

Combine like terms: 9.695359715 + 7 = 16.695359715
x = 16.695359715

Simplifying
x = 16.695359715


Subproblem 2
x + -7 = -9.695359715

Simplifying
x + -7 = -9.695359715

Reorder the terms:
-7 + x = -9.695359715

Solving
-7 + x = -9.695359715

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -9.695359715 + 7

Combine like terms: -7 + 7 = 0
0 + x = -9.695359715 + 7
x = -9.695359715 + 7

Combine like terms: -9.695359715 + 7 = -2.695359715
x = -2.695359715

Simplifying
x = -2.695359715


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.695359715, -2.695359715}
Solution
x = {16.695359715, -2.695359715}

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