x^2+6x+15=-6x+4

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Solution for x^2+6x+15=-6x+4 equation: 


Simplifying
x2 + 6x + 15 = -6x + 4

Reorder the terms:
15 + 6x + x2 = -6x + 4

Reorder the terms:
15 + 6x + x2 = 4 + -6x

Solving
15 + 6x + x2 = 4 + -6x

Solving for variable 'x'.

Reorder the terms:
15 + -4 + 6x + 6x + x2 = 4 + -6x + -4 + 6x

Combine like terms: 15 + -4 = 11
11 + 6x + 6x + x2 = 4 + -6x + -4 + 6x

Combine like terms: 6x + 6x = 12x
11 + 12x + x2 = 4 + -6x + -4 + 6x

Reorder the terms:
11 + 12x + x2 = 4 + -4 + -6x + 6x

Combine like terms: 4 + -4 = 0
11 + 12x + x2 = 0 + -6x + 6x
11 + 12x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
11 + 12x + x2 = 0

Factor a trinomial.
(11 + x)(1 + x) = 0


Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-11, -1}

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