2x^2z+28xz+90z=0

Solution for 2x^2z+28xz+90z=0 equation:

Simplifying
2x2z + 28xz + 90z = 0

Reorder the terms:
28xz + 2x2z + 90z = 0

Solving
28xz + 2x2z + 90z = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2z'.
2z(14x + x2 + 45) = 0

Factor a trinomial.
2z((x + 5)(x + 9)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Add '-1z' to each side of the equation.
z + -1z = 0 + -1z
Remove the zero:
0 = -1z

Simplifying
0 = -1z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(x + 5)' equal to zero and attempt to solve:

Simplifying
x + 5 = 0

Reorder the terms:
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

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

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

Simplifying
x = -5
Subproblem 3
Set the factor '(x + 9)' equal to zero and attempt to solve:

Simplifying
x + 9 = 0

Reorder the terms:
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9
Solution
x = {-5, -9}