(z+4)*((z^2)-3z+2)*5=5*(z+4)

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Solution for (z+4)*((z^2)-3z+2)*5=5*(z+4) equation: 


Simplifying
(z + 4)((z2) + -3z + 2) * 5 = 5(z + 4)

Reorder the terms:
(4 + z)((z2) + -3z + 2) * 5 = 5(z + 4)
(4 + z)(z2 + -3z + 2) * 5 = 5(z + 4)

Reorder the terms:
(4 + z)(2 + -3z + z2) * 5 = 5(z + 4)

Reorder the terms for easier multiplication:
5(4 + z)(2 + -3z + z2) = 5(z + 4)

Multiply (4 + z) * (2 + -3z + z2)
5(4(2 + -3z + z2) + z(2 + -3z + z2)) = 5(z + 4)
5((2 * 4 + -3z * 4 + z2 * 4) + z(2 + -3z + z2)) = 5(z + 4)
5((8 + -12z + 4z2) + z(2 + -3z + z2)) = 5(z + 4)
5(8 + -12z + 4z2 + (2 * z + -3z * z + z2 * z)) = 5(z + 4)
5(8 + -12z + 4z2 + (2z + -3z2 + z3)) = 5(z + 4)

Reorder the terms:
5(8 + -12z + 2z + 4z2 + -3z2 + z3) = 5(z + 4)

Combine like terms: -12z + 2z = -10z
5(8 + -10z + 4z2 + -3z2 + z3) = 5(z + 4)

Combine like terms: 4z2 + -3z2 = 1z2
5(8 + -10z + 1z2 + z3) = 5(z + 4)
(8 * 5 + -10z * 5 + 1z2 * 5 + z3 * 5) = 5(z + 4)
(40 + -50z + 5z2 + 5z3) = 5(z + 4)

Reorder the terms:
40 + -50z + 5z2 + 5z3 = 5(4 + z)
40 + -50z + 5z2 + 5z3 = (4 * 5 + z * 5)
40 + -50z + 5z2 + 5z3 = (20 + 5z)

Solving
40 + -50z + 5z2 + 5z3 = 20 + 5z

Solving for variable 'z'.

Reorder the terms:
40 + -20 + -50z + -5z + 5z2 + 5z3 = 20 + 5z + -20 + -5z

Combine like terms: 40 + -20 = 20
20 + -50z + -5z + 5z2 + 5z3 = 20 + 5z + -20 + -5z

Combine like terms: -50z + -5z = -55z
20 + -55z + 5z2 + 5z3 = 20 + 5z + -20 + -5z

Reorder the terms:
20 + -55z + 5z2 + 5z3 = 20 + -20 + 5z + -5z

Combine like terms: 20 + -20 = 0
20 + -55z + 5z2 + 5z3 = 0 + 5z + -5z
20 + -55z + 5z2 + 5z3 = 5z + -5z

Combine like terms: 5z + -5z = 0
20 + -55z + 5z2 + 5z3 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -11z + z2 + z3) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + -11z + z2 + z3)' equal to zero and attempt to solve:

Simplifying
4 + -11z + z2 + z3 = 0

Solving
4 + -11z + z2 + z3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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