8(z+1)-5(z-1)(z+1)=-4(z-1)

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Solution for 8(z+1)-5(z-1)(z+1)=-4(z-1) equation: 


Simplifying
8(z + 1) + -5(z + -1)(z + 1) = -4(z + -1)

Reorder the terms:
8(1 + z) + -5(z + -1)(z + 1) = -4(z + -1)
(1 * 8 + z * 8) + -5(z + -1)(z + 1) = -4(z + -1)
(8 + 8z) + -5(z + -1)(z + 1) = -4(z + -1)

Reorder the terms:
8 + 8z + -5(-1 + z)(z + 1) = -4(z + -1)

Reorder the terms:
8 + 8z + -5(-1 + z)(1 + z) = -4(z + -1)

Multiply (-1 + z) * (1 + z)
8 + 8z + -5(-1(1 + z) + z(1 + z)) = -4(z + -1)
8 + 8z + -5((1 * -1 + z * -1) + z(1 + z)) = -4(z + -1)
8 + 8z + -5((-1 + -1z) + z(1 + z)) = -4(z + -1)
8 + 8z + -5(-1 + -1z + (1 * z + z * z)) = -4(z + -1)
8 + 8z + -5(-1 + -1z + (1z + z2)) = -4(z + -1)

Combine like terms: -1z + 1z = 0
8 + 8z + -5(-1 + 0 + z2) = -4(z + -1)
8 + 8z + -5(-1 + z2) = -4(z + -1)
8 + 8z + (-1 * -5 + z2 * -5) = -4(z + -1)
8 + 8z + (5 + -5z2) = -4(z + -1)

Reorder the terms:
8 + 5 + 8z + -5z2 = -4(z + -1)

Combine like terms: 8 + 5 = 13
13 + 8z + -5z2 = -4(z + -1)

Reorder the terms:
13 + 8z + -5z2 = -4(-1 + z)
13 + 8z + -5z2 = (-1 * -4 + z * -4)
13 + 8z + -5z2 = (4 + -4z)

Solving
13 + 8z + -5z2 = 4 + -4z

Solving for variable 'z'.

Reorder the terms:
13 + -4 + 8z + 4z + -5z2 = 4 + -4z + -4 + 4z

Combine like terms: 13 + -4 = 9
9 + 8z + 4z + -5z2 = 4 + -4z + -4 + 4z

Combine like terms: 8z + 4z = 12z
9 + 12z + -5z2 = 4 + -4z + -4 + 4z

Reorder the terms:
9 + 12z + -5z2 = 4 + -4 + -4z + 4z

Combine like terms: 4 + -4 = 0
9 + 12z + -5z2 = 0 + -4z + 4z
9 + 12z + -5z2 = -4z + 4z

Combine like terms: -4z + 4z = 0
9 + 12z + -5z2 = 0

Factor a trinomial.
(3 + -1z)(3 + 5z) = 0


Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3

Subproblem 2
Set the factor '(3 + 5z)' equal to zero and attempt to solve:

Simplifying
3 + 5z = 0

Solving
3 + 5z = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5z = 0 + -3
5z = 0 + -3

Combine like terms: 0 + -3 = -3
5z = -3

Divide each side by '5'.
z = -0.6

Simplifying
z = -0.6
Solution
z = {3, -0.6}

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