(p+2)(p-3)+(p+3)(p-4)=p(2p-5)

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Solution for (p+2)(p-3)+(p+3)(p-4)=p(2p-5) equation:


Simplifying
(p + 2)(p + -3) + (p + 3)(p + -4) = p(2p + -5)

Reorder the terms:
(2 + p)(p + -3) + (p + 3)(p + -4) = p(2p + -5)

Reorder the terms:
(2 + p)(-3 + p) + (p + 3)(p + -4) = p(2p + -5)

Multiply (2 + p) * (-3 + p)
(2(-3 + p) + p(-3 + p)) + (p + 3)(p + -4) = p(2p + -5)
((-3 * 2 + p * 2) + p(-3 + p)) + (p + 3)(p + -4) = p(2p + -5)
((-6 + 2p) + p(-3 + p)) + (p + 3)(p + -4) = p(2p + -5)
(-6 + 2p + (-3 * p + p * p)) + (p + 3)(p + -4) = p(2p + -5)
(-6 + 2p + (-3p + p2)) + (p + 3)(p + -4) = p(2p + -5)

Combine like terms: 2p + -3p = -1p
(-6 + -1p + p2) + (p + 3)(p + -4) = p(2p + -5)

Reorder the terms:
-6 + -1p + p2 + (3 + p)(p + -4) = p(2p + -5)

Reorder the terms:
-6 + -1p + p2 + (3 + p)(-4 + p) = p(2p + -5)

Multiply (3 + p) * (-4 + p)
-6 + -1p + p2 + (3(-4 + p) + p(-4 + p)) = p(2p + -5)
-6 + -1p + p2 + ((-4 * 3 + p * 3) + p(-4 + p)) = p(2p + -5)
-6 + -1p + p2 + ((-12 + 3p) + p(-4 + p)) = p(2p + -5)
-6 + -1p + p2 + (-12 + 3p + (-4 * p + p * p)) = p(2p + -5)
-6 + -1p + p2 + (-12 + 3p + (-4p + p2)) = p(2p + -5)

Combine like terms: 3p + -4p = -1p
-6 + -1p + p2 + (-12 + -1p + p2) = p(2p + -5)

Reorder the terms:
-6 + -12 + -1p + -1p + p2 + p2 = p(2p + -5)

Combine like terms: -6 + -12 = -18
-18 + -1p + -1p + p2 + p2 = p(2p + -5)

Combine like terms: -1p + -1p = -2p
-18 + -2p + p2 + p2 = p(2p + -5)

Combine like terms: p2 + p2 = 2p2
-18 + -2p + 2p2 = p(2p + -5)

Reorder the terms:
-18 + -2p + 2p2 = p(-5 + 2p)
-18 + -2p + 2p2 = (-5 * p + 2p * p)
-18 + -2p + 2p2 = (-5p + 2p2)

Add '-2p2' to each side of the equation.
-18 + -2p + 2p2 + -2p2 = -5p + 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-18 + -2p + 0 = -5p + 2p2 + -2p2
-18 + -2p = -5p + 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-18 + -2p = -5p + 0
-18 + -2p = -5p

Solving
-18 + -2p = -5p

Solving for variable 'p'.

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

Add '5p' to each side of the equation.
-18 + -2p + 5p = -5p + 5p

Combine like terms: -2p + 5p = 3p
-18 + 3p = -5p + 5p

Combine like terms: -5p + 5p = 0
-18 + 3p = 0

Add '18' to each side of the equation.
-18 + 18 + 3p = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 3p = 0 + 18
3p = 0 + 18

Combine like terms: 0 + 18 = 18
3p = 18

Divide each side by '3'.
p = 6

Simplifying
p = 6

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