(5p-4)(6p+8)=0

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Solution for (5p-4)(6p+8)=0 equation: 


Simplifying
(5p + -4)(6p + 8) = 0

Reorder the terms:
(-4 + 5p)(6p + 8) = 0

Reorder the terms:
(-4 + 5p)(8 + 6p) = 0

Multiply (-4 + 5p) * (8 + 6p)
(-4(8 + 6p) + 5p * (8 + 6p)) = 0
((8 * -4 + 6p * -4) + 5p * (8 + 6p)) = 0
((-32 + -24p) + 5p * (8 + 6p)) = 0
(-32 + -24p + (8 * 5p + 6p * 5p)) = 0
(-32 + -24p + (40p + 30p2)) = 0

Combine like terms: -24p + 40p = 16p
(-32 + 16p + 30p2) = 0

Solving
-32 + 16p + 30p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 8p + 15p2) = 0

Factor a trinomial.
2((-4 + -3p)(4 + -5p)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3p)' equal to zero and attempt to solve:

Simplifying
-4 + -3p = 0

Solving
-4 + -3p = 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 + -3p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3p = 0 + 4
-3p = 0 + 4

Combine like terms: 0 + 4 = 4
-3p = 4

Divide each side by '-3'.
p = -1.333333333

Simplifying
p = -1.333333333

Subproblem 2
Set the factor '(4 + -5p)' equal to zero and attempt to solve:

Simplifying
4 + -5p = 0

Solving
4 + -5p = 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 + -5p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5p = 0 + -4
-5p = 0 + -4

Combine like terms: 0 + -4 = -4
-5p = -4

Divide each side by '-5'.
p = 0.8

Simplifying
p = 0.8
Solution
p = {-1.333333333, 0.8}

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