x^2+x=-9x-16x

Solution for x^2+x=-9x-16x equation:

Simplifying
x2 + x = -9x + -16x

Reorder the terms:
x + x2 = -9x + -16x

Combine like terms: -9x + -16x = -25x
x + x2 = -25x

Solving
x + x2 = -25x

Solving for variable 'x'.

Reorder the terms:
x + 25x + x2 = -25x + 25x

Combine like terms: x + 25x = 26x
26x + x2 = -25x + 25x

Combine like terms: -25x + 25x = 0
26x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(26 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(26 + x)' equal to zero and attempt to solve:

Simplifying
26 + x = 0

Solving
26 + x = 0

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

Add '-26' to each side of the equation.
26 + -26 + x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + x = 0 + -26
x = 0 + -26

Combine like terms: 0 + -26 = -26
x = -26

Simplifying
x = -26
Solution
x = {0, -26}