6p^2=-(5p+1)

Solution for 6p^2=-(5p+1) equation:

Simplifying
6p2 = -1(5p + 1)

Reorder the terms:
6p2 = -1(1 + 5p)
6p2 = (1 * -1 + 5p * -1)
6p2 = (-1 + -5p)

Solving
6p2 = -1 + -5p

Solving for variable 'p'.

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

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

Combine like terms: -1 + 1 = 0
1 + 5p + 6p2 = 0 + -5p + 5p
1 + 5p + 6p2 = -5p + 5p

Combine like terms: -5p + 5p = 0
1 + 5p + 6p2 = 0

Factor a trinomial.
(1 + 2p)(1 + 3p) = 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 '(1 + 3p)' equal to zero and attempt to solve:

Simplifying
1 + 3p = 0

Solving
1 + 3p = 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 + 3p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3p = 0 + -1
3p = 0 + -1

Combine like terms: 0 + -1 = -1
3p = -1

Divide each side by '3'.
p = -0.3333333333

Simplifying
p = -0.3333333333
Solution
p = {-0.5, -0.3333333333}