x^2+3x-52=-2x-16

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Solution for x^2+3x-52=-2x-16 equation: 


Simplifying
x2 + 3x + -52 = -2x + -16

Reorder the terms:
-52 + 3x + x2 = -2x + -16

Reorder the terms:
-52 + 3x + x2 = -16 + -2x

Solving
-52 + 3x + x2 = -16 + -2x

Solving for variable 'x'.

Reorder the terms:
-52 + 16 + 3x + 2x + x2 = -16 + -2x + 16 + 2x

Combine like terms: -52 + 16 = -36
-36 + 3x + 2x + x2 = -16 + -2x + 16 + 2x

Combine like terms: 3x + 2x = 5x
-36 + 5x + x2 = -16 + -2x + 16 + 2x

Reorder the terms:
-36 + 5x + x2 = -16 + 16 + -2x + 2x

Combine like terms: -16 + 16 = 0
-36 + 5x + x2 = 0 + -2x + 2x
-36 + 5x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-36 + 5x + x2 = 0

Factor a trinomial.
(-9 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-9, 4}

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