-z(z+17)=(19z+36)(1-z)

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Solution for -z(z+17)=(19z+36)(1-z) equation: 


Simplifying
-1z(z + 17) = (19z + 36)(1 + -1z)

Reorder the terms:
-1z(17 + z) = (19z + 36)(1 + -1z)
(17 * -1z + z * -1z) = (19z + 36)(1 + -1z)
(-17z + -1z2) = (19z + 36)(1 + -1z)

Reorder the terms:
-17z + -1z2 = (36 + 19z)(1 + -1z)

Multiply (36 + 19z) * (1 + -1z)
-17z + -1z2 = (36(1 + -1z) + 19z * (1 + -1z))
-17z + -1z2 = ((1 * 36 + -1z * 36) + 19z * (1 + -1z))
-17z + -1z2 = ((36 + -36z) + 19z * (1 + -1z))
-17z + -1z2 = (36 + -36z + (1 * 19z + -1z * 19z))
-17z + -1z2 = (36 + -36z + (19z + -19z2))

Combine like terms: -36z + 19z = -17z
-17z + -1z2 = (36 + -17z + -19z2)

Add '17z' to each side of the equation.
-17z + 17z + -1z2 = 36 + -17z + 17z + -19z2

Combine like terms: -17z + 17z = 0
0 + -1z2 = 36 + -17z + 17z + -19z2
-1z2 = 36 + -17z + 17z + -19z2

Combine like terms: -17z + 17z = 0
-1z2 = 36 + 0 + -19z2
-1z2 = 36 + -19z2

Solving
-1z2 = 36 + -19z2

Solving for variable 'z'.

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

Add '19z2' to each side of the equation.
-1z2 + 19z2 = 36 + -19z2 + 19z2

Combine like terms: -1z2 + 19z2 = 18z2
18z2 = 36 + -19z2 + 19z2

Combine like terms: -19z2 + 19z2 = 0
18z2 = 36 + 0
18z2 = 36

Divide each side by '18'.
z2 = 2

Simplifying
z2 = 2

Take the square root of each side:
z = {-1.414213562, 1.414213562}

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