(pi+1)(pi+4)+3(pi-2)(pi-1)=4pi(pi-6)

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Solution for (pi+1)(pi+4)+3(pi-2)(pi-1)=4pi(pi-6) equation: 


Simplifying
(pi + 1)(pi + 4) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)

Reorder the terms:
(1 + ip)(pi + 4) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)

Reorder the terms:
(1 + ip)(4 + ip) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)

Multiply (1 + ip) * (4 + ip)
(1(4 + ip) + ip(4 + ip)) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)
((4 * 1 + ip * 1) + ip(4 + ip)) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)
((4 + 1ip) + ip(4 + ip)) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)
(4 + 1ip + (4 * ip + ip * ip)) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)
(4 + 1ip + (4ip + i2p2)) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)

Combine like terms: 1ip + 4ip = 5ip
(4 + 5ip + i2p2) + 3(pi + -2)(pi + -1) = 4pi(pi + -6)

Reorder the terms:
4 + 5ip + i2p2 + 3(-2 + ip)(pi + -1) = 4pi(pi + -6)

Reorder the terms:
4 + 5ip + i2p2 + 3(-2 + ip)(-1 + ip) = 4pi(pi + -6)

Multiply (-2 + ip) * (-1 + ip)
4 + 5ip + i2p2 + 3(-2(-1 + ip) + ip(-1 + ip)) = 4pi(pi + -6)
4 + 5ip + i2p2 + 3((-1 * -2 + ip * -2) + ip(-1 + ip)) = 4pi(pi + -6)
4 + 5ip + i2p2 + 3((2 + -2ip) + ip(-1 + ip)) = 4pi(pi + -6)
4 + 5ip + i2p2 + 3(2 + -2ip + (-1 * ip + ip * ip)) = 4pi(pi + -6)
4 + 5ip + i2p2 + 3(2 + -2ip + (-1ip + i2p2)) = 4pi(pi + -6)

Combine like terms: -2ip + -1ip = -3ip
4 + 5ip + i2p2 + 3(2 + -3ip + i2p2) = 4pi(pi + -6)
4 + 5ip + i2p2 + (2 * 3 + -3ip * 3 + i2p2 * 3) = 4pi(pi + -6)
4 + 5ip + i2p2 + (6 + -9ip + 3i2p2) = 4pi(pi + -6)

Reorder the terms:
4 + 6 + 5ip + -9ip + i2p2 + 3i2p2 = 4pi(pi + -6)

Combine like terms: 4 + 6 = 10
10 + 5ip + -9ip + i2p2 + 3i2p2 = 4pi(pi + -6)

Combine like terms: 5ip + -9ip = -4ip
10 + -4ip + i2p2 + 3i2p2 = 4pi(pi + -6)

Combine like terms: i2p2 + 3i2p2 = 4i2p2
10 + -4ip + 4i2p2 = 4pi(pi + -6)

Reorder the terms:
10 + -4ip + 4i2p2 = 4ip(-6 + ip)
10 + -4ip + 4i2p2 = (-6 * 4ip + ip * 4ip)
10 + -4ip + 4i2p2 = (-24ip + 4i2p2)

Add '-4i2p2' to each side of the equation.
10 + -4ip + 4i2p2 + -4i2p2 = -24ip + 4i2p2 + -4i2p2

Combine like terms: 4i2p2 + -4i2p2 = 0
10 + -4ip + 0 = -24ip + 4i2p2 + -4i2p2
10 + -4ip = -24ip + 4i2p2 + -4i2p2

Combine like terms: 4i2p2 + -4i2p2 = 0
10 + -4ip = -24ip + 0
10 + -4ip = -24ip

Solving
10 + -4ip = -24ip

Solving for variable 'i'.

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

Add '24ip' to each side of the equation.
10 + -4ip + 24ip = -24ip + 24ip

Combine like terms: -4ip + 24ip = 20ip
10 + 20ip = -24ip + 24ip

Combine like terms: -24ip + 24ip = 0
10 + 20ip = 0

Add '-10' to each side of the equation.
10 + -10 + 20ip = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 20ip = 0 + -10
20ip = 0 + -10

Combine like terms: 0 + -10 = -10
20ip = -10

Divide each side by '20p'.
i = -0.5p-1

Simplifying
i = -0.5p-1

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