(x-3)(x+3)=-5x-13

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Solution for (x-3)(x+3)=-5x-13 equation: 


Simplifying
(x + -3)(x + 3) = -5x + -13

Reorder the terms:
(-3 + x)(x + 3) = -5x + -13

Reorder the terms:
(-3 + x)(3 + x) = -5x + -13

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x)) = -5x + -13
((3 * -3 + x * -3) + x(3 + x)) = -5x + -13
((-9 + -3x) + x(3 + x)) = -5x + -13
(-9 + -3x + (3 * x + x * x)) = -5x + -13
(-9 + -3x + (3x + x2)) = -5x + -13

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2) = -5x + -13
(-9 + x2) = -5x + -13

Reorder the terms:
-9 + x2 = -13 + -5x

Solving
-9 + x2 = -13 + -5x

Solving for variable 'x'.

Reorder the terms:
-9 + 13 + 5x + x2 = -13 + -5x + 13 + 5x

Combine like terms: -9 + 13 = 4
4 + 5x + x2 = -13 + -5x + 13 + 5x

Reorder the terms:
4 + 5x + x2 = -13 + 13 + -5x + 5x

Combine like terms: -13 + 13 = 0
4 + 5x + x2 = 0 + -5x + 5x
4 + 5x + x2 = -5x + 5x

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

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


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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4

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 = {-4, -1}

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