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

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


Simplifying
(3z + -1u)(5z + 2u) = 0

Reorder the terms:
(-1u + 3z)(5z + 2u) = 0

Reorder the terms:
(-1u + 3z)(2u + 5z) = 0

Multiply (-1u + 3z) * (2u + 5z)
(-1u * (2u + 5z) + 3z * (2u + 5z)) = 0
((2u * -1u + 5z * -1u) + 3z * (2u + 5z)) = 0

Reorder the terms:
((-5uz + -2u2) + 3z * (2u + 5z)) = 0
((-5uz + -2u2) + 3z * (2u + 5z)) = 0
(-5uz + -2u2 + (2u * 3z + 5z * 3z)) = 0
(-5uz + -2u2 + (6uz + 15z2)) = 0

Reorder the terms:
(-5uz + 6uz + -2u2 + 15z2) = 0

Combine like terms: -5uz + 6uz = 1uz
(1uz + -2u2 + 15z2) = 0

Solving
1uz + -2u2 + 15z2 = 0

Solving for variable 'u'.

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

Subproblem 1

Set the factor '(-2u + -5z)' equal to zero and attempt to solve: Simplifying -2u + -5z = 0 Solving -2u + -5z = 0 Move all terms containing u to the left, all other terms to the right. Add '5z' to each side of the equation. -2u + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 -2u + 0 = 0 + 5z -2u = 0 + 5z Remove the zero: -2u = 5z Divide each side by '-2'. u = -2.5z Simplifying u = -2.5z

Subproblem 2

Set the factor '(u + -3z)' equal to zero and attempt to solve: Simplifying u + -3z = 0 Solving u + -3z = 0 Move all terms containing u to the left, all other terms to the right. Add '3z' to each side of the equation. u + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 u + 0 = 0 + 3z u = 0 + 3z Remove the zero: u = 3z Simplifying u = 3z

Solution

u = {-2.5z, 3z}

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