2(x^2+1)=-5x

Solution for 2(x^2+1)=-5x equation:

Simplifying
2(x2 + 1) = -5x

Reorder the terms:
2(1 + x2) = -5x
(1 * 2 + x2 * 2) = -5x
(2 + 2x2) = -5x

Solving
2 + 2x2 = -5x

Solving for variable 'x'.

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

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

Factor a trinomial.
(2 + x)(1 + 2x) = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2, -0.5}