4p^2+3=8p

Solution for 4p^2+3=8p equation:

Simplifying
4p2 + 3 = 8p

Reorder the terms:
3 + 4p2 = 8p

Solving
3 + 4p2 = 8p

Solving for variable 'p'.

Reorder the terms:
3 + -8p + 4p2 = 8p + -8p

Combine like terms: 8p + -8p = 0
3 + -8p + 4p2 = 0

Factor a trinomial.
(1 + -2p)(3 + -2p) = 0

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

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

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

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

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
Subproblem 2
Set the factor '(3 + -2p)' equal to zero and attempt to solve:

Simplifying
3 + -2p = 0

Solving
3 + -2p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2p = 0 + -3
-2p = 0 + -3

Combine like terms: 0 + -3 = -3
-2p = -3

Divide each side by '-2'.
p = 1.5

Simplifying
p = 1.5
Solution
p = {0.5, 1.5}