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

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


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

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

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

Multiply (5 + p) * (-8 + 7p)
(5(-8 + 7p) + p(-8 + 7p)) = 0
((-8 * 5 + 7p * 5) + p(-8 + 7p)) = 0
((-40 + 35p) + p(-8 + 7p)) = 0
(-40 + 35p + (-8 * p + 7p * p)) = 0
(-40 + 35p + (-8p + 7p2)) = 0

Combine like terms: 35p + -8p = 27p
(-40 + 27p + 7p2) = 0

Solving
-40 + 27p + 7p2 = 0

Solving for variable 'p'.

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


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

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
p = -5

Simplifying
p = -5

Subproblem 2
Set the factor '(8 + -7p)' equal to zero and attempt to solve:

Simplifying
8 + -7p = 0

Solving
8 + -7p = 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 + -7p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7p = 0 + -8
-7p = 0 + -8

Combine like terms: 0 + -8 = -8
-7p = -8

Divide each side by '-7'.
p = 1.142857143

Simplifying
p = 1.142857143
Solution
p = {-5, 1.142857143}

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