30X^2+45X-1=-1

Solution for 30X^2+45X-1=-1 equation:

Simplifying
30X2 + 45X + -1 = -1

Reorder the terms:
-1 + 45X + 30X2 = -1

Add '1' to each side of the equation.
-1 + 45X + 1 + 30X2 = -1 + 1

Reorder the terms:
-1 + 1 + 45X + 30X2 = -1 + 1

Combine like terms: -1 + 1 = 0
0 + 45X + 30X2 = -1 + 1
45X + 30X2 = -1 + 1

Combine like terms: -1 + 1 = 0
45X + 30X2 = 0

Solving
45X + 30X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '15X'.
15X(3 + 2X) = 0

Ignore the factor 15.
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 '(3 + 2X)' equal to zero and attempt to solve:

Simplifying
3 + 2X = 0

Solving
3 + 2X = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2X = 0 + -3
2X = 0 + -3

Combine like terms: 0 + -3 = -3
2X = -3

Divide each side by '2'.
X = -1.5

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