(z+5)*(z-8)=-3(z+8)

Solution for (z+5)*(z-8)=-3(z+8) equation:

Simplifying
(z + 5)(z + -8) = -3(z + 8)

Reorder the terms:
(5 + z)(z + -8) = -3(z + 8)

Reorder the terms:
(5 + z)(-8 + z) = -3(z + 8)

Multiply (5 + z) * (-8 + z)
(5(-8 + z) + z(-8 + z)) = -3(z + 8)
((-8 * 5 + z * 5) + z(-8 + z)) = -3(z + 8)
((-40 + 5z) + z(-8 + z)) = -3(z + 8)
(-40 + 5z + (-8 * z + z * z)) = -3(z + 8)
(-40 + 5z + (-8z + z2)) = -3(z + 8)

Combine like terms: 5z + -8z = -3z
(-40 + -3z + z2) = -3(z + 8)

Reorder the terms:
-40 + -3z + z2 = -3(8 + z)
-40 + -3z + z2 = (8 * -3 + z * -3)
-40 + -3z + z2 = (-24 + -3z)

Add '3z' to each side of the equation.
-40 + -3z + 3z + z2 = -24 + -3z + 3z

Combine like terms: -3z + 3z = 0
-40 + 0 + z2 = -24 + -3z + 3z
-40 + z2 = -24 + -3z + 3z

Combine like terms: -3z + 3z = 0
-40 + z2 = -24 + 0
-40 + z2 = -24

Solving
-40 + z2 = -24

Solving for variable 'z'.

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

Add '40' to each side of the equation.
-40 + 40 + z2 = -24 + 40

Combine like terms: -40 + 40 = 0
0 + z2 = -24 + 40
z2 = -24 + 40

Combine like terms: -24 + 40 = 16
z2 = 16

Simplifying
z2 = 16

Take the square root of each side:
z = {-4, 4}