4p^2-5=6p-1

Solution for 4p^2-5=6p-1 equation:

Simplifying
4p2 + -5 = 6p + -1

Reorder the terms:
-5 + 4p2 = 6p + -1

Reorder the terms:
-5 + 4p2 = -1 + 6p

Solving
-5 + 4p2 = -1 + 6p

Solving for variable 'p'.

Reorder the terms:
-5 + 1 + -6p + 4p2 = -1 + 6p + 1 + -6p

Combine like terms: -5 + 1 = -4
-4 + -6p + 4p2 = -1 + 6p + 1 + -6p

Reorder the terms:
-4 + -6p + 4p2 = -1 + 1 + 6p + -6p

Combine like terms: -1 + 1 = 0
-4 + -6p + 4p2 = 0 + 6p + -6p
-4 + -6p + 4p2 = 6p + -6p

Combine like terms: 6p + -6p = 0
-4 + -6p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -3p + 2p2) = 0

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

Ignore the factor 2.
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 '(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 = {-0.5, 2}