z^2+5z-4=(2z+1)(z-4)

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Solution for z^2+5z-4=(2z+1)(z-4) equation: 


Simplifying
z2 + 5z + -4 = (2z + 1)(z + -4)

Reorder the terms:
-4 + 5z + z2 = (2z + 1)(z + -4)

Reorder the terms:
-4 + 5z + z2 = (1 + 2z)(z + -4)

Reorder the terms:
-4 + 5z + z2 = (1 + 2z)(-4 + z)

Multiply (1 + 2z) * (-4 + z)
-4 + 5z + z2 = (1(-4 + z) + 2z * (-4 + z))
-4 + 5z + z2 = ((-4 * 1 + z * 1) + 2z * (-4 + z))
-4 + 5z + z2 = ((-4 + 1z) + 2z * (-4 + z))
-4 + 5z + z2 = (-4 + 1z + (-4 * 2z + z * 2z))
-4 + 5z + z2 = (-4 + 1z + (-8z + 2z2))

Combine like terms: 1z + -8z = -7z
-4 + 5z + z2 = (-4 + -7z + 2z2)

Add '4' to each side of the equation.
-4 + 5z + 4 + z2 = -4 + -7z + 4 + 2z2

Reorder the terms:
-4 + 4 + 5z + z2 = -4 + -7z + 4 + 2z2

Combine like terms: -4 + 4 = 0
0 + 5z + z2 = -4 + -7z + 4 + 2z2
5z + z2 = -4 + -7z + 4 + 2z2

Reorder the terms:
5z + z2 = -4 + 4 + -7z + 2z2

Combine like terms: -4 + 4 = 0
5z + z2 = 0 + -7z + 2z2
5z + z2 = -7z + 2z2

Solving
5z + z2 = -7z + 2z2

Solving for variable 'z'.

Reorder the terms:
5z + 7z + z2 + -2z2 = -7z + 2z2 + 7z + -2z2

Combine like terms: 5z + 7z = 12z
12z + z2 + -2z2 = -7z + 2z2 + 7z + -2z2

Combine like terms: z2 + -2z2 = -1z2
12z + -1z2 = -7z + 2z2 + 7z + -2z2

Reorder the terms:
12z + -1z2 = -7z + 7z + 2z2 + -2z2

Combine like terms: -7z + 7z = 0
12z + -1z2 = 0 + 2z2 + -2z2
12z + -1z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
12z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(12 + -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 '(12 + -1z)' equal to zero and attempt to solve:

Simplifying
12 + -1z = 0

Solving
12 + -1z = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1z = 0 + -12
-1z = 0 + -12

Combine like terms: 0 + -12 = -12
-1z = -12

Divide each side by '-1'.
z = 12

Simplifying
z = 12
Solution
z = {0, 12}

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