(3z+4)(3z+4)-(3z-8)(3z+8)=4z

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Solution for (3z+4)(3z+4)-(3z-8)(3z+8)=4z equation: 


Simplifying
(3z + 4)(3z + 4) + -1(3z + -8)(3z + 8) = 4z

Reorder the terms:
(4 + 3z)(3z + 4) + -1(3z + -8)(3z + 8) = 4z

Reorder the terms:
(4 + 3z)(4 + 3z) + -1(3z + -8)(3z + 8) = 4z

Multiply (4 + 3z) * (4 + 3z)
(4(4 + 3z) + 3z * (4 + 3z)) + -1(3z + -8)(3z + 8) = 4z
((4 * 4 + 3z * 4) + 3z * (4 + 3z)) + -1(3z + -8)(3z + 8) = 4z
((16 + 12z) + 3z * (4 + 3z)) + -1(3z + -8)(3z + 8) = 4z
(16 + 12z + (4 * 3z + 3z * 3z)) + -1(3z + -8)(3z + 8) = 4z
(16 + 12z + (12z + 9z2)) + -1(3z + -8)(3z + 8) = 4z

Combine like terms: 12z + 12z = 24z
(16 + 24z + 9z2) + -1(3z + -8)(3z + 8) = 4z

Reorder the terms:
16 + 24z + 9z2 + -1(-8 + 3z)(3z + 8) = 4z

Reorder the terms:
16 + 24z + 9z2 + -1(-8 + 3z)(8 + 3z) = 4z

Multiply (-8 + 3z) * (8 + 3z)
16 + 24z + 9z2 + -1(-8(8 + 3z) + 3z * (8 + 3z)) = 4z
16 + 24z + 9z2 + -1((8 * -8 + 3z * -8) + 3z * (8 + 3z)) = 4z
16 + 24z + 9z2 + -1((-64 + -24z) + 3z * (8 + 3z)) = 4z
16 + 24z + 9z2 + -1(-64 + -24z + (8 * 3z + 3z * 3z)) = 4z
16 + 24z + 9z2 + -1(-64 + -24z + (24z + 9z2)) = 4z

Combine like terms: -24z + 24z = 0
16 + 24z + 9z2 + -1(-64 + 0 + 9z2) = 4z
16 + 24z + 9z2 + -1(-64 + 9z2) = 4z
16 + 24z + 9z2 + (-64 * -1 + 9z2 * -1) = 4z
16 + 24z + 9z2 + (64 + -9z2) = 4z

Reorder the terms:
16 + 64 + 24z + 9z2 + -9z2 = 4z

Combine like terms: 16 + 64 = 80
80 + 24z + 9z2 + -9z2 = 4z

Combine like terms: 9z2 + -9z2 = 0
80 + 24z + 0 = 4z
80 + 24z = 4z

Solving
80 + 24z = 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
80 + 24z + -4z = 4z + -4z

Combine like terms: 24z + -4z = 20z
80 + 20z = 4z + -4z

Combine like terms: 4z + -4z = 0
80 + 20z = 0

Add '-80' to each side of the equation.
80 + -80 + 20z = 0 + -80

Combine like terms: 80 + -80 = 0
0 + 20z = 0 + -80
20z = 0 + -80

Combine like terms: 0 + -80 = -80
20z = -80

Divide each side by '20'.
z = -4

Simplifying
z = -4

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