42p^2-90p-108=0

Solution for 42p^2-90p-108=0 equation:

Simplifying
42p2 + -90p + -108 = 0

Reorder the terms:
-108 + -90p + 42p2 = 0

Solving
-108 + -90p + 42p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-18 + -15p + 7p2) = 0

Factor a trinomial.
6((-6 + -7p)(3 + -1p)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-6 + -7p)' equal to zero and attempt to solve:

Simplifying
-6 + -7p = 0

Solving
-6 + -7p = 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 + -7p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7p = 0 + 6
-7p = 0 + 6

Combine like terms: 0 + 6 = 6
-7p = 6

Divide each side by '-7'.
p = -0.8571428571

Simplifying
p = -0.8571428571
Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-0.8571428571, 3}