6(p^2+1)-(2p-4)(3p+2)=3(5p+21)

Solution for 6(p^2+1)-(2p-4)(3p+2)=3(5p+21) equation:

Simplifying
6(p2 + 1) + -1(2p + -4)(3p + 2) = 3(5p + 21)

Reorder the terms:
6(1 + p2) + -1(2p + -4)(3p + 2) = 3(5p + 21)
(1 * 6 + p2 * 6) + -1(2p + -4)(3p + 2) = 3(5p + 21)
(6 + 6p2) + -1(2p + -4)(3p + 2) = 3(5p + 21)

Reorder the terms:
6 + 6p2 + -1(-4 + 2p)(3p + 2) = 3(5p + 21)

Reorder the terms:
6 + 6p2 + -1(-4 + 2p)(2 + 3p) = 3(5p + 21)

Multiply (-4 + 2p) * (2 + 3p)
6 + 6p2 + -1(-4(2 + 3p) + 2p * (2 + 3p)) = 3(5p + 21)
6 + 6p2 + -1((2 * -4 + 3p * -4) + 2p * (2 + 3p)) = 3(5p + 21)
6 + 6p2 + -1((-8 + -12p) + 2p * (2 + 3p)) = 3(5p + 21)
6 + 6p2 + -1(-8 + -12p + (2 * 2p + 3p * 2p)) = 3(5p + 21)
6 + 6p2 + -1(-8 + -12p + (4p + 6p2)) = 3(5p + 21)

Combine like terms: -12p + 4p = -8p
6 + 6p2 + -1(-8 + -8p + 6p2) = 3(5p + 21)
6 + 6p2 + (-8 * -1 + -8p * -1 + 6p2 * -1) = 3(5p + 21)
6 + 6p2 + (8 + 8p + -6p2) = 3(5p + 21)

Reorder the terms:
6 + 8 + 8p + 6p2 + -6p2 = 3(5p + 21)

Combine like terms: 6 + 8 = 14
14 + 8p + 6p2 + -6p2 = 3(5p + 21)

Combine like terms: 6p2 + -6p2 = 0
14 + 8p + 0 = 3(5p + 21)
14 + 8p = 3(5p + 21)

Reorder the terms:
14 + 8p = 3(21 + 5p)
14 + 8p = (21 * 3 + 5p * 3)
14 + 8p = (63 + 15p)

Solving
14 + 8p = 63 + 15p

Solving for variable 'p'.

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

Add '-15p' to each side of the equation.
14 + 8p + -15p = 63 + 15p + -15p

Combine like terms: 8p + -15p = -7p
14 + -7p = 63 + 15p + -15p

Combine like terms: 15p + -15p = 0
14 + -7p = 63 + 0
14 + -7p = 63

Add '-14' to each side of the equation.
14 + -14 + -7p = 63 + -14

Combine like terms: 14 + -14 = 0
0 + -7p = 63 + -14
-7p = 63 + -14

Combine like terms: 63 + -14 = 49
-7p = 49

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

Simplifying
p = -7