18-3z(2z+1)-[3-2(z+2)(z-3)]=18-6z-4(z-5)(z+2)

Solution for 18-3z(2z+1)-[3-2(z+2)(z-3)]=18-6z-4(z-5)(z+2) equation:

Simplifying
18 + -3z(2z + 1) + -1[3 + -2(z + 2)(z + -3)] = 18 + -6z + -4(z + -5)(z + 2)

Reorder the terms:
18 + -3z(1 + 2z) + -1[3 + -2(z + 2)(z + -3)] = 18 + -6z + -4(z + -5)(z + 2)
18 + (1 * -3z + 2z * -3z) + -1[3 + -2(z + 2)(z + -3)] = 18 + -6z + -4(z + -5)(z + 2)
18 + (-3z + -6z2) + -1[3 + -2(z + 2)(z + -3)] = 18 + -6z + -4(z + -5)(z + 2)

Reorder the terms:
18 + -3z + -6z2 + -1[3 + -2(2 + z)(z + -3)] = 18 + -6z + -4(z + -5)(z + 2)

Reorder the terms:
18 + -3z + -6z2 + -1[3 + -2(2 + z)(-3 + z)] = 18 + -6z + -4(z + -5)(z + 2)

Multiply (2 + z) * (-3 + z)
18 + -3z + -6z2 + -1[3 + -2(2(-3 + z) + z(-3 + z))] = 18 + -6z + -4(z + -5)(z + 2)
18 + -3z + -6z2 + -1[3 + -2((-3 * 2 + z * 2) + z(-3 + z))] = 18 + -6z + -4(z + -5)(z + 2)
18 + -3z + -6z2 + -1[3 + -2((-6 + 2z) + z(-3 + z))] = 18 + -6z + -4(z + -5)(z + 2)
18 + -3z + -6z2 + -1[3 + -2(-6 + 2z + (-3 * z + z * z))] = 18 + -6z + -4(z + -5)(z + 2)
18 + -3z + -6z2 + -1[3 + -2(-6 + 2z + (-3z + z2))] = 18 + -6z + -4(z + -5)(z + 2)

Combine like terms: 2z + -3z = -1z
18 + -3z + -6z2 + -1[3 + -2(-6 + -1z + z2)] = 18 + -6z + -4(z + -5)(z + 2)
18 + -3z + -6z2 + -1[3 + (-6 * -2 + -1z * -2 + z2 * -2)] = 18 + -6z + -4(z + -5)(z + 2)
18 + -3z + -6z2 + -1[3 + (12 + 2z + -2z2)] = 18 + -6z + -4(z + -5)(z + 2)

Combine like terms: 3 + 12 = 15
18 + -3z + -6z2 + -1[15 + 2z + -2z2] = 18 + -6z + -4(z + -5)(z + 2)
18 + -3z + -6z2 + [15 * -1 + 2z * -1 + -2z2 * -1] = 18 + -6z + -4(z + -5)(z + 2)
18 + -3z + -6z2 + [-15 + -2z + 2z2] = 18 + -6z + -4(z + -5)(z + 2)

Reorder the terms:
18 + -15 + -3z + -2z + -6z2 + 2z2 = 18 + -6z + -4(z + -5)(z + 2)

Combine like terms: 18 + -15 = 3
3 + -3z + -2z + -6z2 + 2z2 = 18 + -6z + -4(z + -5)(z + 2)

Combine like terms: -3z + -2z = -5z
3 + -5z + -6z2 + 2z2 = 18 + -6z + -4(z + -5)(z + 2)

Combine like terms: -6z2 + 2z2 = -4z2
3 + -5z + -4z2 = 18 + -6z + -4(z + -5)(z + 2)

Reorder the terms:
3 + -5z + -4z2 = 18 + -6z + -4(-5 + z)(z + 2)

Reorder the terms:
3 + -5z + -4z2 = 18 + -6z + -4(-5 + z)(2 + z)

Multiply (-5 + z) * (2 + z)
3 + -5z + -4z2 = 18 + -6z + -4(-5(2 + z) + z(2 + z))
3 + -5z + -4z2 = 18 + -6z + -4((2 * -5 + z * -5) + z(2 + z))
3 + -5z + -4z2 = 18 + -6z + -4((-10 + -5z) + z(2 + z))
3 + -5z + -4z2 = 18 + -6z + -4(-10 + -5z + (2 * z + z * z))
3 + -5z + -4z2 = 18 + -6z + -4(-10 + -5z + (2z + z2))

Combine like terms: -5z + 2z = -3z
3 + -5z + -4z2 = 18 + -6z + -4(-10 + -3z + z2)
3 + -5z + -4z2 = 18 + -6z + (-10 * -4 + -3z * -4 + z2 * -4)
3 + -5z + -4z2 = 18 + -6z + (40 + 12z + -4z2)

Reorder the terms:
3 + -5z + -4z2 = 18 + 40 + -6z + 12z + -4z2

Combine like terms: 18 + 40 = 58
3 + -5z + -4z2 = 58 + -6z + 12z + -4z2

Combine like terms: -6z + 12z = 6z
3 + -5z + -4z2 = 58 + 6z + -4z2

Add '4z2' to each side of the equation.
3 + -5z + -4z2 + 4z2 = 58 + 6z + -4z2 + 4z2

Combine like terms: -4z2 + 4z2 = 0
3 + -5z + 0 = 58 + 6z + -4z2 + 4z2
3 + -5z = 58 + 6z + -4z2 + 4z2

Combine like terms: -4z2 + 4z2 = 0
3 + -5z = 58 + 6z + 0
3 + -5z = 58 + 6z

Solving
3 + -5z = 58 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
3 + -5z + -6z = 58 + 6z + -6z

Combine like terms: -5z + -6z = -11z
3 + -11z = 58 + 6z + -6z

Combine like terms: 6z + -6z = 0
3 + -11z = 58 + 0
3 + -11z = 58

Add '-3' to each side of the equation.
3 + -3 + -11z = 58 + -3

Combine like terms: 3 + -3 = 0
0 + -11z = 58 + -3
-11z = 58 + -3

Combine like terms: 58 + -3 = 55
-11z = 55

Divide each side by '-11'.
z = -5

Simplifying
z = -5