(2p+7)(6p-7)=0

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Solution for (2p+7)(6p-7)=0 equation: 


Simplifying
(2p + 7)(6p + -7) = 0

Reorder the terms:
(7 + 2p)(6p + -7) = 0

Reorder the terms:
(7 + 2p)(-7 + 6p) = 0

Multiply (7 + 2p) * (-7 + 6p)
(7(-7 + 6p) + 2p * (-7 + 6p)) = 0
((-7 * 7 + 6p * 7) + 2p * (-7 + 6p)) = 0
((-49 + 42p) + 2p * (-7 + 6p)) = 0
(-49 + 42p + (-7 * 2p + 6p * 2p)) = 0
(-49 + 42p + (-14p + 12p2)) = 0

Combine like terms: 42p + -14p = 28p
(-49 + 28p + 12p2) = 0

Solving
-49 + 28p + 12p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-7 + -2p)(7 + -6p) = 0


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

Simplifying
-7 + -2p = 0

Solving
-7 + -2p = 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 + -2p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2p = 0 + 7
-2p = 0 + 7

Combine like terms: 0 + 7 = 7
-2p = 7

Divide each side by '-2'.
p = -3.5

Simplifying
p = -3.5

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 = {-3.5, 1.166666667}

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