(5z-3)(z+4)-(5z-3)(z-3)=0

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Solution for (5z-3)(z+4)-(5z-3)(z-3)=0 equation: 


Simplifying
(5z + -3)(z + 4) + -1(5z + -3)(z + -3) = 0

Reorder the terms:
(-3 + 5z)(z + 4) + -1(5z + -3)(z + -3) = 0

Reorder the terms:
(-3 + 5z)(4 + z) + -1(5z + -3)(z + -3) = 0

Multiply (-3 + 5z) * (4 + z)
(-3(4 + z) + 5z * (4 + z)) + -1(5z + -3)(z + -3) = 0
((4 * -3 + z * -3) + 5z * (4 + z)) + -1(5z + -3)(z + -3) = 0
((-12 + -3z) + 5z * (4 + z)) + -1(5z + -3)(z + -3) = 0
(-12 + -3z + (4 * 5z + z * 5z)) + -1(5z + -3)(z + -3) = 0
(-12 + -3z + (20z + 5z2)) + -1(5z + -3)(z + -3) = 0

Combine like terms: -3z + 20z = 17z
(-12 + 17z + 5z2) + -1(5z + -3)(z + -3) = 0

Reorder the terms:
-12 + 17z + 5z2 + -1(-3 + 5z)(z + -3) = 0

Reorder the terms:
-12 + 17z + 5z2 + -1(-3 + 5z)(-3 + z) = 0

Multiply (-3 + 5z) * (-3 + z)
-12 + 17z + 5z2 + -1(-3(-3 + z) + 5z * (-3 + z)) = 0
-12 + 17z + 5z2 + -1((-3 * -3 + z * -3) + 5z * (-3 + z)) = 0
-12 + 17z + 5z2 + -1((9 + -3z) + 5z * (-3 + z)) = 0
-12 + 17z + 5z2 + -1(9 + -3z + (-3 * 5z + z * 5z)) = 0
-12 + 17z + 5z2 + -1(9 + -3z + (-15z + 5z2)) = 0

Combine like terms: -3z + -15z = -18z
-12 + 17z + 5z2 + -1(9 + -18z + 5z2) = 0
-12 + 17z + 5z2 + (9 * -1 + -18z * -1 + 5z2 * -1) = 0
-12 + 17z + 5z2 + (-9 + 18z + -5z2) = 0

Reorder the terms:
-12 + -9 + 17z + 18z + 5z2 + -5z2 = 0

Combine like terms: -12 + -9 = -21
-21 + 17z + 18z + 5z2 + -5z2 = 0

Combine like terms: 17z + 18z = 35z
-21 + 35z + 5z2 + -5z2 = 0

Combine like terms: 5z2 + -5z2 = 0
-21 + 35z + 0 = 0
-21 + 35z = 0

Solving
-21 + 35z = 0

Solving for variable 'z'.

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

Add '21' to each side of the equation.
-21 + 21 + 35z = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 35z = 0 + 21
35z = 0 + 21

Combine like terms: 0 + 21 = 21
35z = 21

Divide each side by '35'.
z = 0.6

Simplifying
z = 0.6

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