-x^2+19=-2x^2-7x+13

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Solution for -x^2+19=-2x^2-7x+13 equation: 


Simplifying
-1x2 + 19 = -2x2 + -7x + 13

Reorder the terms:
19 + -1x2 = -2x2 + -7x + 13

Reorder the terms:
19 + -1x2 = 13 + -7x + -2x2

Solving
19 + -1x2 = 13 + -7x + -2x2

Solving for variable 'x'.

Reorder the terms:
19 + -13 + 7x + -1x2 + 2x2 = 13 + -7x + -2x2 + -13 + 7x + 2x2

Combine like terms: 19 + -13 = 6
6 + 7x + -1x2 + 2x2 = 13 + -7x + -2x2 + -13 + 7x + 2x2

Combine like terms: -1x2 + 2x2 = 1x2
6 + 7x + 1x2 = 13 + -7x + -2x2 + -13 + 7x + 2x2

Reorder the terms:
6 + 7x + 1x2 = 13 + -13 + -7x + 7x + -2x2 + 2x2

Combine like terms: 13 + -13 = 0
6 + 7x + 1x2 = 0 + -7x + 7x + -2x2 + 2x2
6 + 7x + 1x2 = -7x + 7x + -2x2 + 2x2

Combine like terms: -7x + 7x = 0
6 + 7x + 1x2 = 0 + -2x2 + 2x2
6 + 7x + 1x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
6 + 7x + 1x2 = 0

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


Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6

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 = {-6, -1}

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