x^2+1.5*x=0

Solution for x^2+1.5*x=0 equation:

Simplifying
x2 + 1.5x = 0

Reorder the terms:
1.5x + x2 = 0

Solving
1.5x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1.5 + 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 '(1.5 + x)' equal to zero and attempt to solve:

Simplifying
1.5 + x = 0

Solving
1.5 + x = 0

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 0 + -1.5
x = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
x = -1.5

Simplifying
x = -1.5
Solution
x = {0, -1.5}