(8z-3)(3z+4)=(6z-5)(4z+9)

Solution for (8z-3)(3z+4)=(6z-5)(4z+9) equation:

Simplifying
(8z + -3)(3z + 4) = (6z + -5)(4z + 9)

Reorder the terms:
(-3 + 8z)(3z + 4) = (6z + -5)(4z + 9)

Reorder the terms:
(-3 + 8z)(4 + 3z) = (6z + -5)(4z + 9)

Multiply (-3 + 8z) * (4 + 3z)
(-3(4 + 3z) + 8z * (4 + 3z)) = (6z + -5)(4z + 9)
((4 * -3 + 3z * -3) + 8z * (4 + 3z)) = (6z + -5)(4z + 9)
((-12 + -9z) + 8z * (4 + 3z)) = (6z + -5)(4z + 9)
(-12 + -9z + (4 * 8z + 3z * 8z)) = (6z + -5)(4z + 9)
(-12 + -9z + (32z + 24z2)) = (6z + -5)(4z + 9)

Combine like terms: -9z + 32z = 23z
(-12 + 23z + 24z2) = (6z + -5)(4z + 9)

Reorder the terms:
-12 + 23z + 24z2 = (-5 + 6z)(4z + 9)

Reorder the terms:
-12 + 23z + 24z2 = (-5 + 6z)(9 + 4z)

Multiply (-5 + 6z) * (9 + 4z)
-12 + 23z + 24z2 = (-5(9 + 4z) + 6z * (9 + 4z))
-12 + 23z + 24z2 = ((9 * -5 + 4z * -5) + 6z * (9 + 4z))
-12 + 23z + 24z2 = ((-45 + -20z) + 6z * (9 + 4z))
-12 + 23z + 24z2 = (-45 + -20z + (9 * 6z + 4z * 6z))
-12 + 23z + 24z2 = (-45 + -20z + (54z + 24z2))

Combine like terms: -20z + 54z = 34z
-12 + 23z + 24z2 = (-45 + 34z + 24z2)

Add '-24z2' to each side of the equation.
-12 + 23z + 24z2 + -24z2 = -45 + 34z + 24z2 + -24z2

Combine like terms: 24z2 + -24z2 = 0
-12 + 23z + 0 = -45 + 34z + 24z2 + -24z2
-12 + 23z = -45 + 34z + 24z2 + -24z2

Combine like terms: 24z2 + -24z2 = 0
-12 + 23z = -45 + 34z + 0
-12 + 23z = -45 + 34z

Solving
-12 + 23z = -45 + 34z

Solving for variable 'z'.

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

Add '-34z' to each side of the equation.
-12 + 23z + -34z = -45 + 34z + -34z

Combine like terms: 23z + -34z = -11z
-12 + -11z = -45 + 34z + -34z

Combine like terms: 34z + -34z = 0
-12 + -11z = -45 + 0
-12 + -11z = -45

Add '12' to each side of the equation.
-12 + 12 + -11z = -45 + 12

Combine like terms: -12 + 12 = 0
0 + -11z = -45 + 12
-11z = -45 + 12

Combine like terms: -45 + 12 = -33
-11z = -33

Divide each side by '-11'.
z = 3

Simplifying
z = 3