(z+5)(z-4)+4z^2=(5z+3)(z-4)+2(z-4)+64

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Solution for (z+5)(z-4)+4z^2=(5z+3)(z-4)+2(z-4)+64 equation: 


Simplifying
(z + 5)(z + -4) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64

Reorder the terms:
(5 + z)(z + -4) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64

Reorder the terms:
(5 + z)(-4 + z) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64

Multiply (5 + z) * (-4 + z)
(5(-4 + z) + z(-4 + z)) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64
((-4 * 5 + z * 5) + z(-4 + z)) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64
((-20 + 5z) + z(-4 + z)) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64
(-20 + 5z + (-4 * z + z * z)) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64
(-20 + 5z + (-4z + z2)) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64

Combine like terms: 5z + -4z = 1z
(-20 + 1z + z2) + 4z2 = (5z + 3)(z + -4) + 2(z + -4) + 64

Combine like terms: z2 + 4z2 = 5z2
-20 + 1z + 5z2 = (5z + 3)(z + -4) + 2(z + -4) + 64

Reorder the terms:
-20 + 1z + 5z2 = (3 + 5z)(z + -4) + 2(z + -4) + 64

Reorder the terms:
-20 + 1z + 5z2 = (3 + 5z)(-4 + z) + 2(z + -4) + 64

Multiply (3 + 5z) * (-4 + z)
-20 + 1z + 5z2 = (3(-4 + z) + 5z * (-4 + z)) + 2(z + -4) + 64
-20 + 1z + 5z2 = ((-4 * 3 + z * 3) + 5z * (-4 + z)) + 2(z + -4) + 64
-20 + 1z + 5z2 = ((-12 + 3z) + 5z * (-4 + z)) + 2(z + -4) + 64
-20 + 1z + 5z2 = (-12 + 3z + (-4 * 5z + z * 5z)) + 2(z + -4) + 64
-20 + 1z + 5z2 = (-12 + 3z + (-20z + 5z2)) + 2(z + -4) + 64

Combine like terms: 3z + -20z = -17z
-20 + 1z + 5z2 = (-12 + -17z + 5z2) + 2(z + -4) + 64

Reorder the terms:
-20 + 1z + 5z2 = -12 + -17z + 5z2 + 2(-4 + z) + 64
-20 + 1z + 5z2 = -12 + -17z + 5z2 + (-4 * 2 + z * 2) + 64
-20 + 1z + 5z2 = -12 + -17z + 5z2 + (-8 + 2z) + 64

Reorder the terms:
-20 + 1z + 5z2 = -12 + -8 + 64 + -17z + 2z + 5z2

Combine like terms: -12 + -8 = -20
-20 + 1z + 5z2 = -20 + 64 + -17z + 2z + 5z2

Combine like terms: -20 + 64 = 44
-20 + 1z + 5z2 = 44 + -17z + 2z + 5z2

Combine like terms: -17z + 2z = -15z
-20 + 1z + 5z2 = 44 + -15z + 5z2

Add '-5z2' to each side of the equation.
-20 + 1z + 5z2 + -5z2 = 44 + -15z + 5z2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
-20 + 1z + 0 = 44 + -15z + 5z2 + -5z2
-20 + 1z = 44 + -15z + 5z2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
-20 + 1z = 44 + -15z + 0
-20 + 1z = 44 + -15z

Solving
-20 + 1z = 44 + -15z

Solving for variable 'z'.

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

Add '15z' to each side of the equation.
-20 + 1z + 15z = 44 + -15z + 15z

Combine like terms: 1z + 15z = 16z
-20 + 16z = 44 + -15z + 15z

Combine like terms: -15z + 15z = 0
-20 + 16z = 44 + 0
-20 + 16z = 44

Add '20' to each side of the equation.
-20 + 20 + 16z = 44 + 20

Combine like terms: -20 + 20 = 0
0 + 16z = 44 + 20
16z = 44 + 20

Combine like terms: 44 + 20 = 64
16z = 64

Divide each side by '16'.
z = 4

Simplifying
z = 4

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