p(4p+7)=2

Solution for p(4p+7)=2 equation:

Simplifying
p(4p + 7) = 2

Reorder the terms:
p(7 + 4p) = 2
(7 * p + 4p * p) = 2
(7p + 4p2) = 2

Solving
7p + 4p2 = 2

Solving for variable 'p'.

Reorder the terms:
-2 + 7p + 4p2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 7p + 4p2 = 0

Factor a trinomial.
(-2 + -1p)(1 + -4p) = 0

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

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2
Subproblem 2
Set the factor '(1 + -4p)' equal to zero and attempt to solve:

Simplifying
1 + -4p = 0

Solving
1 + -4p = 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 + -4p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4p = 0 + -1
-4p = 0 + -1

Combine like terms: 0 + -1 = -1
-4p = -1

Divide each side by '-4'.
p = 0.25

Simplifying
p = 0.25
Solution
p = {-2, 0.25}