z^2+8z-20=(2z+5)(z-4)

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Solution for z^2+8z-20=(2z+5)(z-4) equation: 


Simplifying
z2 + 8z + -20 = (2z + 5)(z + -4)

Reorder the terms:
-20 + 8z + z2 = (2z + 5)(z + -4)

Reorder the terms:
-20 + 8z + z2 = (5 + 2z)(z + -4)

Reorder the terms:
-20 + 8z + z2 = (5 + 2z)(-4 + z)

Multiply (5 + 2z) * (-4 + z)
-20 + 8z + z2 = (5(-4 + z) + 2z * (-4 + z))
-20 + 8z + z2 = ((-4 * 5 + z * 5) + 2z * (-4 + z))
-20 + 8z + z2 = ((-20 + 5z) + 2z * (-4 + z))
-20 + 8z + z2 = (-20 + 5z + (-4 * 2z + z * 2z))
-20 + 8z + z2 = (-20 + 5z + (-8z + 2z2))

Combine like terms: 5z + -8z = -3z
-20 + 8z + z2 = (-20 + -3z + 2z2)

Add '20' to each side of the equation.
-20 + 8z + 20 + z2 = -20 + -3z + 20 + 2z2

Reorder the terms:
-20 + 20 + 8z + z2 = -20 + -3z + 20 + 2z2

Combine like terms: -20 + 20 = 0
0 + 8z + z2 = -20 + -3z + 20 + 2z2
8z + z2 = -20 + -3z + 20 + 2z2

Reorder the terms:
8z + z2 = -20 + 20 + -3z + 2z2

Combine like terms: -20 + 20 = 0
8z + z2 = 0 + -3z + 2z2
8z + z2 = -3z + 2z2

Solving
8z + z2 = -3z + 2z2

Solving for variable 'z'.

Reorder the terms:
8z + 3z + z2 + -2z2 = -3z + 2z2 + 3z + -2z2

Combine like terms: 8z + 3z = 11z
11z + z2 + -2z2 = -3z + 2z2 + 3z + -2z2

Combine like terms: z2 + -2z2 = -1z2
11z + -1z2 = -3z + 2z2 + 3z + -2z2

Reorder the terms:
11z + -1z2 = -3z + 3z + 2z2 + -2z2

Combine like terms: -3z + 3z = 0
11z + -1z2 = 0 + 2z2 + -2z2
11z + -1z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
11z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(11 + -1z) = 0


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 '(11 + -1z)' equal to zero and attempt to solve:

Simplifying
11 + -1z = 0

Solving
11 + -1z = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1z = 0 + -11
-1z = 0 + -11

Combine like terms: 0 + -11 = -11
-1z = -11

Divide each side by '-1'.
z = 11

Simplifying
z = 11
Solution
z = {0, 11}

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