8(p-0.25)=4p(2p-0.5)

Solution for 8(p-0.25)=4p(2p-0.5) equation:

Simplifying
8(p + -0.25) = 4p(2p + -0.5)

Reorder the terms:
8(-0.25 + p) = 4p(2p + -0.5)
(-0.25 * 8 + p * 8) = 4p(2p + -0.5)
(-2 + 8p) = 4p(2p + -0.5)

Reorder the terms:
-2 + 8p = 4p(-0.5 + 2p)
-2 + 8p = (-0.5 * 4p + 2p * 4p)
-2 + 8p = (-2p + 8p2)

Solving
-2 + 8p = -2p + 8p2

Solving for variable 'p'.

Combine like terms: 8p + 2p = 10p
-2 + 10p + -8p2 = -2p + 8p2 + 2p + -8p2

Reorder the terms:
-2 + 10p + -8p2 = -2p + 2p + 8p2 + -8p2

Combine like terms: -2p + 2p = 0
-2 + 10p + -8p2 = 0 + 8p2 + -8p2
-2 + 10p + -8p2 = 8p2 + -8p2

Combine like terms: 8p2 + -8p2 = 0
-2 + 10p + -8p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 5p + -4p2) = 0

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

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

Simplifying
-1 + p = 0

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

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

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

Simplifying
p = 1
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 = {1, 0.25}