(p-7)(5p-8)=0

Solution for (p-7)(5p-8)=0 equation:

Simplifying
(p + -7)(5p + -8) = 0

Reorder the terms:
(-7 + p)(5p + -8) = 0

Reorder the terms:
(-7 + p)(-8 + 5p) = 0

Multiply (-7 + p) * (-8 + 5p)
(-7(-8 + 5p) + p(-8 + 5p)) = 0
((-8 * -7 + 5p * -7) + p(-8 + 5p)) = 0
((56 + -35p) + p(-8 + 5p)) = 0
(56 + -35p + (-8 * p + 5p * p)) = 0
(56 + -35p + (-8p + 5p2)) = 0

Combine like terms: -35p + -8p = -43p
(56 + -43p + 5p2) = 0

Solving
56 + -43p + 5p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(8 + -5p)(7 + -1p) = 0

Subproblem 1
Set the factor '(8 + -5p)' equal to zero and attempt to solve:

Simplifying
8 + -5p = 0

Solving
8 + -5p = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5p = 0 + -8
-5p = 0 + -8

Combine like terms: 0 + -8 = -8
-5p = -8

Divide each side by '-5'.
p = 1.6

Simplifying
p = 1.6
Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve:

Simplifying
7 + -1p = 0

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

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

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

Divide each side by '-1'.
p = 7

Simplifying
p = 7
Solution
p = {1.6, 7}