4p^2-3p+4=5

Solution for 4p^2-3p+4=5 equation:

Simplifying
4p2 + -3p + 4 = 5

Reorder the terms:
4 + -3p + 4p2 = 5

Solving
4 + -3p + 4p2 = 5

Solving for variable 'p'.

Reorder the terms:
4 + -5 + -3p + 4p2 = 5 + -5

Combine like terms: 4 + -5 = -1
-1 + -3p + 4p2 = 5 + -5

Combine like terms: 5 + -5 = 0
-1 + -3p + 4p2 = 0

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

Subproblem 1
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
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 = {-0.25, 1}