Math

Question Solve for uu where (5u2)(3u+4)=0(5u-2)(-3u+4)=0. Write the solutions as integers or simplified fractions.

Studdy Solution

STEP 1

Assumptions
1. We have a quadratic equation in the form of a product of two linear factors equal to zero.
2. To find the solutions for uu, we will use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

STEP 2

Apply the zero product property to the given equation.
(5u2)(3u+4)=0(5u - 2)(-3u + 4) = 0

STEP 3

Set each factor equal to zero and solve for uu separately.
5u2=0or3u+4=05u - 2 = 0 \quad \text{or} \quad -3u + 4 = 0

STEP 4

Solve the first equation for uu.
5u2=05u - 2 = 0

STEP 5

Add 2 to both sides of the equation.
5u=25u = 2

STEP 6

Divide both sides by 5 to isolate uu.
u=25u = \frac{2}{5}

STEP 7

Solve the second equation for uu.
3u+4=0-3u + 4 = 0

STEP 8

Subtract 4 from both sides of the equation.
3u=4-3u = -4

STEP 9

Divide both sides by -3 to isolate uu.
u=43u = \frac{4}{-3}

STEP 10

Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, if necessary. In this case, the fraction is already in simplest form.
u=43u = \frac{-4}{3}

STEP 11

Combine the solutions from STEP_6 and STEP_10.
The solutions for uu are:
u=25 or u=43u = \frac{2}{5} \text{ or } u = \frac{-4}{3}

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