4p^2-p=105

Solution for 4p^2-p=105 equation:

Simplifying
4p2 + -1p = 105

Reorder the terms:
-1p + 4p2 = 105

Solving
-1p + 4p2 = 105

Solving for variable 'p'.

Reorder the terms:
-105 + -1p + 4p2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + -1p + 4p2 = 0

Factor a trinomial.
(-5 + -1p)(21 + -4p) = 0

Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve:

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
p = -5

Simplifying
p = -5
Subproblem 2
Set the factor '(21 + -4p)' equal to zero and attempt to solve:

Simplifying
21 + -4p = 0

Solving
21 + -4p = 0

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

Add '-21' to each side of the equation.
21 + -21 + -4p = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -4p = 0 + -21
-4p = 0 + -21

Combine like terms: 0 + -21 = -21
-4p = -21

Divide each side by '-4'.
p = 5.25

Simplifying
p = 5.25
Solution
p = {-5, 5.25}