4p+3=6p(p+1)-1

Solution for 4p+3=6p(p+1)-1 equation:

Simplifying
4p + 3 = 6p(p + 1) + -1

Reorder the terms:
3 + 4p = 6p(p + 1) + -1

Reorder the terms:
3 + 4p = 6p(1 + p) + -1
3 + 4p = (1 * 6p + p * 6p) + -1
3 + 4p = (6p + 6p2) + -1

Reorder the terms:
3 + 4p = -1 + 6p + 6p2

Solving
3 + 4p = -1 + 6p + 6p2

Solving for variable 'p'.

Reorder the terms:
3 + 1 + 4p + -6p + -6p2 = -1 + 6p + 6p2 + 1 + -6p + -6p2

Combine like terms: 3 + 1 = 4
4 + 4p + -6p + -6p2 = -1 + 6p + 6p2 + 1 + -6p + -6p2

Combine like terms: 4p + -6p = -2p
4 + -2p + -6p2 = -1 + 6p + 6p2 + 1 + -6p + -6p2

Reorder the terms:
4 + -2p + -6p2 = -1 + 1 + 6p + -6p + 6p2 + -6p2

Combine like terms: -1 + 1 = 0
4 + -2p + -6p2 = 0 + 6p + -6p + 6p2 + -6p2
4 + -2p + -6p2 = 6p + -6p + 6p2 + -6p2

Combine like terms: 6p + -6p = 0
4 + -2p + -6p2 = 0 + 6p2 + -6p2
4 + -2p + -6p2 = 6p2 + -6p2

Combine like terms: 6p2 + -6p2 = 0
4 + -2p + -6p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -1p + -3p2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -3p)' equal to zero and attempt to solve:

Simplifying
2 + -3p = 0

Solving
2 + -3p = 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 + -3p = 0 + -2

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

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

Divide each side by '-3'.
p = 0.6666666667

Simplifying
p = 0.6666666667
Subproblem 2
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
Solution
p = {0.6666666667, -1}