(3z-2)(2z-3)=2(z-3)(3z+5)+1

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Solution for (3z-2)(2z-3)=2(z-3)(3z+5)+1 equation: 


Simplifying
(3z + -2)(2z + -3) = 2(z + -3)(3z + 5) + 1

Reorder the terms:
(-2 + 3z)(2z + -3) = 2(z + -3)(3z + 5) + 1

Reorder the terms:
(-2 + 3z)(-3 + 2z) = 2(z + -3)(3z + 5) + 1

Multiply (-2 + 3z) * (-3 + 2z)
(-2(-3 + 2z) + 3z * (-3 + 2z)) = 2(z + -3)(3z + 5) + 1
((-3 * -2 + 2z * -2) + 3z * (-3 + 2z)) = 2(z + -3)(3z + 5) + 1
((6 + -4z) + 3z * (-3 + 2z)) = 2(z + -3)(3z + 5) + 1
(6 + -4z + (-3 * 3z + 2z * 3z)) = 2(z + -3)(3z + 5) + 1
(6 + -4z + (-9z + 6z2)) = 2(z + -3)(3z + 5) + 1

Combine like terms: -4z + -9z = -13z
(6 + -13z + 6z2) = 2(z + -3)(3z + 5) + 1

Reorder the terms:
6 + -13z + 6z2 = 2(-3 + z)(3z + 5) + 1

Reorder the terms:
6 + -13z + 6z2 = 2(-3 + z)(5 + 3z) + 1

Multiply (-3 + z) * (5 + 3z)
6 + -13z + 6z2 = 2(-3(5 + 3z) + z(5 + 3z)) + 1
6 + -13z + 6z2 = 2((5 * -3 + 3z * -3) + z(5 + 3z)) + 1
6 + -13z + 6z2 = 2((-15 + -9z) + z(5 + 3z)) + 1
6 + -13z + 6z2 = 2(-15 + -9z + (5 * z + 3z * z)) + 1
6 + -13z + 6z2 = 2(-15 + -9z + (5z + 3z2)) + 1

Combine like terms: -9z + 5z = -4z
6 + -13z + 6z2 = 2(-15 + -4z + 3z2) + 1
6 + -13z + 6z2 = (-15 * 2 + -4z * 2 + 3z2 * 2) + 1
6 + -13z + 6z2 = (-30 + -8z + 6z2) + 1

Reorder the terms:
6 + -13z + 6z2 = -30 + 1 + -8z + 6z2

Combine like terms: -30 + 1 = -29
6 + -13z + 6z2 = -29 + -8z + 6z2

Add '-6z2' to each side of the equation.
6 + -13z + 6z2 + -6z2 = -29 + -8z + 6z2 + -6z2

Combine like terms: 6z2 + -6z2 = 0
6 + -13z + 0 = -29 + -8z + 6z2 + -6z2
6 + -13z = -29 + -8z + 6z2 + -6z2

Combine like terms: 6z2 + -6z2 = 0
6 + -13z = -29 + -8z + 0
6 + -13z = -29 + -8z

Solving
6 + -13z = -29 + -8z

Solving for variable 'z'.

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

Add '8z' to each side of the equation.
6 + -13z + 8z = -29 + -8z + 8z

Combine like terms: -13z + 8z = -5z
6 + -5z = -29 + -8z + 8z

Combine like terms: -8z + 8z = 0
6 + -5z = -29 + 0
6 + -5z = -29

Add '-6' to each side of the equation.
6 + -6 + -5z = -29 + -6

Combine like terms: 6 + -6 = 0
0 + -5z = -29 + -6
-5z = -29 + -6

Combine like terms: -29 + -6 = -35
-5z = -35

Divide each side by '-5'.
z = 7

Simplifying
z = 7

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