(6p-7)(7p+6)=0

Solution for (6p-7)(7p+6)=0 equation:

Simplifying
(6p + -7)(7p + 6) = 0

Reorder the terms:
(-7 + 6p)(7p + 6) = 0

Reorder the terms:
(-7 + 6p)(6 + 7p) = 0

Multiply (-7 + 6p) * (6 + 7p)
(-7(6 + 7p) + 6p * (6 + 7p)) = 0
((6 * -7 + 7p * -7) + 6p * (6 + 7p)) = 0
((-42 + -49p) + 6p * (6 + 7p)) = 0
(-42 + -49p + (6 * 6p + 7p * 6p)) = 0
(-42 + -49p + (36p + 42p2)) = 0

Combine like terms: -49p + 36p = -13p
(-42 + -13p + 42p2) = 0

Solving
-42 + -13p + 42p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-6 + -7p)(7 + -6p) = 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 '(7 + -6p)' equal to zero and attempt to solve:

Simplifying
7 + -6p = 0

Solving
7 + -6p = 0

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

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

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

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

Divide each side by '-6'.
p = 1.166666667

Simplifying
p = 1.166666667
Solution
p = {-0.8571428571, 1.166666667}