(6z-5)(3z-4)=90

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Solution for (6z-5)(3z-4)=90 equation: 


Simplifying
(6z + -5)(3z + -4) = 90

Reorder the terms:
(-5 + 6z)(3z + -4) = 90

Reorder the terms:
(-5 + 6z)(-4 + 3z) = 90

Multiply (-5 + 6z) * (-4 + 3z)
(-5(-4 + 3z) + 6z * (-4 + 3z)) = 90
((-4 * -5 + 3z * -5) + 6z * (-4 + 3z)) = 90
((20 + -15z) + 6z * (-4 + 3z)) = 90
(20 + -15z + (-4 * 6z + 3z * 6z)) = 90
(20 + -15z + (-24z + 18z2)) = 90

Combine like terms: -15z + -24z = -39z
(20 + -39z + 18z2) = 90

Solving
20 + -39z + 18z2 = 90

Solving for variable 'z'.

Reorder the terms:
20 + -90 + -39z + 18z2 = 90 + -90

Combine like terms: 20 + -90 = -70
-70 + -39z + 18z2 = 90 + -90

Combine like terms: 90 + -90 = 0
-70 + -39z + 18z2 = 0

Factor a trinomial.
(-7 + -6z)(10 + -3z) = 0


Subproblem 1
Set the factor '(-7 + -6z)' equal to zero and attempt to solve:

Simplifying
-7 + -6z = 0

Solving
-7 + -6z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6z = 0 + 7
-6z = 0 + 7

Combine like terms: 0 + 7 = 7
-6z = 7

Divide each side by '-6'.
z = -1.166666667

Simplifying
z = -1.166666667

Subproblem 2
Set the factor '(10 + -3z)' equal to zero and attempt to solve:

Simplifying
10 + -3z = 0

Solving
10 + -3z = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3z = 0 + -10
-3z = 0 + -10

Combine like terms: 0 + -10 = -10
-3z = -10

Divide each side by '-3'.
z = 3.333333333

Simplifying
z = 3.333333333
Solution
z = {-1.166666667, 3.333333333}

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