45x^2-2x-15=0

Solution for 45x^2-2x-15=0 equation:

Simplifying
45x2 + -2x + -15 = 0

Reorder the terms:
-15 + -2x + 45x2 = 0

Solving
-15 + -2x + 45x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -9x)(3 + -5x) = 0

Subproblem 1
Set the factor '(-5 + -9x)' equal to zero and attempt to solve:

Simplifying
-5 + -9x = 0

Solving
-5 + -9x = 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 + -9x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -9x = 0 + 5
-9x = 0 + 5

Combine like terms: 0 + 5 = 5
-9x = 5

Divide each side by '-9'.
x = -0.5555555556

Simplifying
x = -0.5555555556
Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-0.5555555556, 0.6}