(2z+7)(3z-4)=

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Solution for (2z+7)(3z-4)= equation:


Simplifying
(2z + 7)(3z + -4) = 0

Reorder the terms:
(7 + 2z)(3z + -4) = 0

Reorder the terms:
(7 + 2z)(-4 + 3z) = 0

Multiply (7 + 2z) * (-4 + 3z)
(7(-4 + 3z) + 2z * (-4 + 3z)) = 0
((-4 * 7 + 3z * 7) + 2z * (-4 + 3z)) = 0
((-28 + 21z) + 2z * (-4 + 3z)) = 0
(-28 + 21z + (-4 * 2z + 3z * 2z)) = 0
(-28 + 21z + (-8z + 6z2)) = 0

Combine like terms: 21z + -8z = 13z
(-28 + 13z + 6z2) = 0

Solving
-28 + 13z + 6z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -2z)(4 + -3z) = 0


Subproblem 1
Set the factor '(-7 + -2z)' equal to zero and attempt to solve:

Simplifying
-7 + -2z = 0

Solving
-7 + -2z = 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 + -2z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2z = 0 + 7
-2z = 0 + 7

Combine like terms: 0 + 7 = 7
-2z = 7

Divide each side by '-2'.
z = -3.5

Simplifying
z = -3.5

Subproblem 2
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
Solution
z = {-3.5, 1.333333333}

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