20p^2+6p=6p^2-13p+3

Solution for 20p^2+6p=6p^2-13p+3 equation:

Simplifying
20p2 + 6p = 6p2 + -13p + 3

Reorder the terms:
6p + 20p2 = 6p2 + -13p + 3

Reorder the terms:
6p + 20p2 = 3 + -13p + 6p2

Solving
6p + 20p2 = 3 + -13p + 6p2

Solving for variable 'p'.

Reorder the terms:
-3 + 6p + 13p + 20p2 + -6p2 = 3 + -13p + 6p2 + -3 + 13p + -6p2

Combine like terms: 6p + 13p = 19p
-3 + 19p + 20p2 + -6p2 = 3 + -13p + 6p2 + -3 + 13p + -6p2

Combine like terms: 20p2 + -6p2 = 14p2
-3 + 19p + 14p2 = 3 + -13p + 6p2 + -3 + 13p + -6p2

Reorder the terms:
-3 + 19p + 14p2 = 3 + -3 + -13p + 13p + 6p2 + -6p2

Combine like terms: 3 + -3 = 0
-3 + 19p + 14p2 = 0 + -13p + 13p + 6p2 + -6p2
-3 + 19p + 14p2 = -13p + 13p + 6p2 + -6p2

Combine like terms: -13p + 13p = 0
-3 + 19p + 14p2 = 0 + 6p2 + -6p2
-3 + 19p + 14p2 = 6p2 + -6p2

Combine like terms: 6p2 + -6p2 = 0
-3 + 19p + 14p2 = 0

Factor a trinomial.
(-3 + -2p)(1 + -7p) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -7p)' equal to zero and attempt to solve:

Simplifying
1 + -7p = 0

Solving
1 + -7p = 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 + -7p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7p = 0 + -1
-7p = 0 + -1

Combine like terms: 0 + -1 = -1
-7p = -1

Divide each side by '-7'.
p = 0.1428571429

Simplifying
p = 0.1428571429
Solution
p = {-1.5, 0.1428571429}