(2z+5w)(3z-4w)=

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Solution for (2z+5w)(3z-4w)= equation: 


Simplifying
(2z + 5w)(3z + -4w) = 0

Reorder the terms:
(5w + 2z)(3z + -4w) = 0

Reorder the terms:
(5w + 2z)(-4w + 3z) = 0

Multiply (5w + 2z) * (-4w + 3z)
(5w * (-4w + 3z) + 2z * (-4w + 3z)) = 0
((-4w * 5w + 3z * 5w) + 2z * (-4w + 3z)) = 0

Reorder the terms:
((15wz + -20w2) + 2z * (-4w + 3z)) = 0
((15wz + -20w2) + 2z * (-4w + 3z)) = 0
(15wz + -20w2 + (-4w * 2z + 3z * 2z)) = 0
(15wz + -20w2 + (-8wz + 6z2)) = 0

Reorder the terms:
(15wz + -8wz + -20w2 + 6z2) = 0

Combine like terms: 15wz + -8wz = 7wz
(7wz + -20w2 + 6z2) = 0

Solving
7wz + -20w2 + 6z2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5w + -2z)(4w + -3z) = 0


Subproblem 1
Set the factor '(-5w + -2z)' equal to zero and attempt to solve:

Simplifying
-5w + -2z = 0

Solving
-5w + -2z = 0

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

Add '2z' to each side of the equation.
-5w + -2z + 2z = 0 + 2z

Combine like terms: -2z + 2z = 0
-5w + 0 = 0 + 2z
-5w = 0 + 2z
Remove the zero:
-5w = 2z

Divide each side by '-5'.
w = -0.4z

Simplifying
w = -0.4z

Subproblem 2
Set the factor '(4w + -3z)' equal to zero and attempt to solve:

Simplifying
4w + -3z = 0

Solving
4w + -3z = 0

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

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

Combine like terms: -3z + 3z = 0
4w + 0 = 0 + 3z
4w = 0 + 3z
Remove the zero:
4w = 3z

Divide each side by '4'.
w = 0.75z

Simplifying
w = 0.75z
Solution
w = {-0.4z, 0.75z}

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