0=3x^2+12x+15

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Solution for 0=3x^2+12x+15 equation: 


Simplifying
0 = 3x2 + 12x + 15

Reorder the terms:
0 = 15 + 12x + 3x2

Solving
0 = 15 + 12x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + -12x + -3x2 = 15 + 12x + 3x2 + -15 + -12x + -3x2

Reorder the terms:
-15 + -12x + -3x2 = 15 + -15 + 12x + -12x + 3x2 + -3x2

Combine like terms: 15 + -15 = 0
-15 + -12x + -3x2 = 0 + 12x + -12x + 3x2 + -3x2
-15 + -12x + -3x2 = 12x + -12x + 3x2 + -3x2

Combine like terms: 12x + -12x = 0
-15 + -12x + -3x2 = 0 + 3x2 + -3x2
-15 + -12x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-15 + -12x + -3x2 = 0

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

Ignore the factor -3.

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

Simplifying
5 + 4x + x2 = 0

Solving
5 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 4x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 4x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x + x2 = 0 + -5
4x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
4x + x2 = -5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -5 + 4

Reorder the terms:
4 + 4x + x2 = -5 + 4

Combine like terms: -5 + 4 = -1
4 + 4x + x2 = -1

Factor a perfect square on the left side:
(x + 2)(x + 2) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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