2(3z+5)(3z+5)=7(3z+5)-5

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Solution for 2(3z+5)(3z+5)=7(3z+5)-5 equation: 


Simplifying
2(3z + 5)(3z + 5) = 7(3z + 5) + -5

Reorder the terms:
2(5 + 3z)(3z + 5) = 7(3z + 5) + -5

Reorder the terms:
2(5 + 3z)(5 + 3z) = 7(3z + 5) + -5

Multiply (5 + 3z) * (5 + 3z)
2(5(5 + 3z) + 3z * (5 + 3z)) = 7(3z + 5) + -5
2((5 * 5 + 3z * 5) + 3z * (5 + 3z)) = 7(3z + 5) + -5
2((25 + 15z) + 3z * (5 + 3z)) = 7(3z + 5) + -5
2(25 + 15z + (5 * 3z + 3z * 3z)) = 7(3z + 5) + -5
2(25 + 15z + (15z + 9z2)) = 7(3z + 5) + -5

Combine like terms: 15z + 15z = 30z
2(25 + 30z + 9z2) = 7(3z + 5) + -5
(25 * 2 + 30z * 2 + 9z2 * 2) = 7(3z + 5) + -5
(50 + 60z + 18z2) = 7(3z + 5) + -5

Reorder the terms:
50 + 60z + 18z2 = 7(5 + 3z) + -5
50 + 60z + 18z2 = (5 * 7 + 3z * 7) + -5
50 + 60z + 18z2 = (35 + 21z) + -5

Reorder the terms:
50 + 60z + 18z2 = 35 + -5 + 21z

Combine like terms: 35 + -5 = 30
50 + 60z + 18z2 = 30 + 21z

Solving
50 + 60z + 18z2 = 30 + 21z

Solving for variable 'z'.

Reorder the terms:
50 + -30 + 60z + -21z + 18z2 = 30 + 21z + -30 + -21z

Combine like terms: 50 + -30 = 20
20 + 60z + -21z + 18z2 = 30 + 21z + -30 + -21z

Combine like terms: 60z + -21z = 39z
20 + 39z + 18z2 = 30 + 21z + -30 + -21z

Reorder the terms:
20 + 39z + 18z2 = 30 + -30 + 21z + -21z

Combine like terms: 30 + -30 = 0
20 + 39z + 18z2 = 0 + 21z + -21z
20 + 39z + 18z2 = 21z + -21z

Combine like terms: 21z + -21z = 0
20 + 39z + 18z2 = 0

Factor a trinomial.
(4 + 3z)(5 + 6z) = 0


Subproblem 1
Set the factor '(4 + 3z)' equal to zero and attempt to solve:

Simplifying
4 + 3z = 0

Solving
4 + 3z = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3z = 0 + -4
3z = 0 + -4

Combine like terms: 0 + -4 = -4
3z = -4

Divide each side by '3'.
z = -1.333333333

Simplifying
z = -1.333333333

Subproblem 2
Set the factor '(5 + 6z)' equal to zero and attempt to solve:

Simplifying
5 + 6z = 0

Solving
5 + 6z = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6z = 0 + -5

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

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

Divide each side by '6'.
z = -0.8333333333

Simplifying
z = -0.8333333333
Solution
z = {-1.333333333, -0.8333333333}

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