5p^2t^2+25pt-30=0

Solution for 5p^2t^2+25pt-30=0 equation:

Simplifying
5p2t2 + 25pt + -30 = 0

Reorder the terms:
-30 + 25pt + 5p2t2 = 0

Solving
-30 + 25pt + 5p2t2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 5pt + p2t2) = 0

Factor a trinomial.
5((-6 + -1pt)(1 + -1pt)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -1pt)' equal to zero and attempt to solve:

Simplifying
-6 + -1pt = 0

Solving
-6 + -1pt = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1pt = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1pt = 0 + 6
-1pt = 0 + 6

Combine like terms: 0 + 6 = 6
-1pt = 6

Divide each side by '-1t'.
p = -6t-1

Simplifying
p = -6t-1
Subproblem 2
Set the factor '(1 + -1pt)' equal to zero and attempt to solve:

Simplifying
1 + -1pt = 0

Solving
1 + -1pt = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1pt = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1pt = 0 + -1
-1pt = 0 + -1

Combine like terms: 0 + -1 = -1
-1pt = -1

Divide each side by '-1t'.
p = t-1

Simplifying
p = t-1
Solution
p = {-6t-1, t-1}