52x+147=-x^2

Solution for 52x+147=-x^2 equation:

Simplifying
52x + 147 = -1x2

Reorder the terms:
147 + 52x = -1x2

Solving
147 + 52x = -1x2

Solving for variable 'x'.

Combine like terms: -1x2 + x2 = 0
147 + 52x + x2 = 0

Factor a trinomial.
(49 + x)(3 + x) = 0

Subproblem 1
Set the factor '(49 + x)' equal to zero and attempt to solve:

Simplifying
49 + x = 0

Solving
49 + x = 0

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

Add '-49' to each side of the equation.
49 + -49 + x = 0 + -49

Combine like terms: 49 + -49 = 0
0 + x = 0 + -49
x = 0 + -49

Combine like terms: 0 + -49 = -49
x = -49

Simplifying
x = -49
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-49, -3}