4p^2+7p=30

Solution for 4p^2+7p=30 equation:

Simplifying
4p2 + 7p = 30

Reorder the terms:
7p + 4p2 = 30

Solving
7p + 4p2 = 30

Solving for variable 'p'.

Reorder the terms:
-30 + 7p + 4p2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 7p + 4p2 = 0

Factor a trinomial.
(-15 + -4p)(2 + -1p) = 0

Subproblem 1
Set the factor '(-15 + -4p)' equal to zero and attempt to solve:

Simplifying
-15 + -4p = 0

Solving
-15 + -4p = 0

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

Add '15' to each side of the equation.
-15 + 15 + -4p = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4p = 0 + 15
-4p = 0 + 15

Combine like terms: 0 + 15 = 15
-4p = 15

Divide each side by '-4'.
p = -3.75

Simplifying
p = -3.75
Subproblem 2
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
Solution
p = {-3.75, 2}