7p^2+35p-42=0

Solution for 7p^2+35p-42=0 equation:

Simplifying
7p2 + 35p + -42 = 0

Reorder the terms:
-42 + 35p + 7p2 = 0

Solving
-42 + 35p + 7p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + 5p + p2) = 0

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

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

Simplifying
-6 + -1p = 0

Solving
-6 + -1p = 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 + -1p = 0 + 6

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

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

Divide each side by '-1'.
p = -6

Simplifying
p = -6
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:

Simplifying
1 + -1p = 0

Solving
1 + -1p = 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 + -1p = 0 + -1

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

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

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

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