7p^2=2(11p+12)

Solution for 7p^2=2(11p+12) equation:

Simplifying
7p2 = 2(11p + 12)

Reorder the terms:
7p2 = 2(12 + 11p)
7p2 = (12 * 2 + 11p * 2)
7p2 = (24 + 22p)

Solving
7p2 = 24 + 22p

Solving for variable 'p'.

Reorder the terms:
-24 + -22p + 7p2 = 24 + 22p + -24 + -22p

Reorder the terms:
-24 + -22p + 7p2 = 24 + -24 + 22p + -22p

Combine like terms: 24 + -24 = 0
-24 + -22p + 7p2 = 0 + 22p + -22p
-24 + -22p + 7p2 = 22p + -22p

Combine like terms: 22p + -22p = 0
-24 + -22p + 7p2 = 0

Factor a trinomial.
(-6 + -7p)(4 + -1p) = 0

Subproblem 1
Set the factor '(-6 + -7p)' equal to zero and attempt to solve:

Simplifying
-6 + -7p = 0

Solving
-6 + -7p = 0

Move all terms containing p to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -7p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7p = 0 + 6
-7p = 0 + 6

Combine like terms: 0 + 6 = 6
-7p = 6

Divide each side by '-7'.
p = -0.8571428571

Simplifying
p = -0.8571428571
Subproblem 2
Set the factor '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

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

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

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {-0.8571428571, 4}