(3z-2)(3z+8)=(z-4)(z+4)

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Solution for (3z-2)(3z+8)=(z-4)(z+4) equation: 


Simplifying
(3z + -2)(3z + 8) = (z + -4)(z + 4)

Reorder the terms:
(-2 + 3z)(3z + 8) = (z + -4)(z + 4)

Reorder the terms:
(-2 + 3z)(8 + 3z) = (z + -4)(z + 4)

Multiply (-2 + 3z) * (8 + 3z)
(-2(8 + 3z) + 3z * (8 + 3z)) = (z + -4)(z + 4)
((8 * -2 + 3z * -2) + 3z * (8 + 3z)) = (z + -4)(z + 4)
((-16 + -6z) + 3z * (8 + 3z)) = (z + -4)(z + 4)
(-16 + -6z + (8 * 3z + 3z * 3z)) = (z + -4)(z + 4)
(-16 + -6z + (24z + 9z2)) = (z + -4)(z + 4)

Combine like terms: -6z + 24z = 18z
(-16 + 18z + 9z2) = (z + -4)(z + 4)

Reorder the terms:
-16 + 18z + 9z2 = (-4 + z)(z + 4)

Reorder the terms:
-16 + 18z + 9z2 = (-4 + z)(4 + z)

Multiply (-4 + z) * (4 + z)
-16 + 18z + 9z2 = (-4(4 + z) + z(4 + z))
-16 + 18z + 9z2 = ((4 * -4 + z * -4) + z(4 + z))
-16 + 18z + 9z2 = ((-16 + -4z) + z(4 + z))
-16 + 18z + 9z2 = (-16 + -4z + (4 * z + z * z))
-16 + 18z + 9z2 = (-16 + -4z + (4z + z2))

Combine like terms: -4z + 4z = 0
-16 + 18z + 9z2 = (-16 + 0 + z2)
-16 + 18z + 9z2 = (-16 + z2)

Add '16' to each side of the equation.
-16 + 18z + 16 + 9z2 = -16 + 16 + z2

Reorder the terms:
-16 + 16 + 18z + 9z2 = -16 + 16 + z2

Combine like terms: -16 + 16 = 0
0 + 18z + 9z2 = -16 + 16 + z2
18z + 9z2 = -16 + 16 + z2

Combine like terms: -16 + 16 = 0
18z + 9z2 = 0 + z2
18z + 9z2 = z2

Solving
18z + 9z2 = z2

Solving for variable 'z'.

Combine like terms: 9z2 + -1z2 = 8z2
18z + 8z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
18z + 8z2 = 0

Factor out the Greatest Common Factor (GCF), '2z'.
2z(9 + 4z) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0

Subproblem 2
Set the factor '(9 + 4z)' equal to zero and attempt to solve:

Simplifying
9 + 4z = 0

Solving
9 + 4z = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4z = 0 + -9
4z = 0 + -9

Combine like terms: 0 + -9 = -9
4z = -9

Divide each side by '4'.
z = -2.25

Simplifying
z = -2.25
Solution
z = {0, -2.25}

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