What are the solutions to the equation (2x+3)/6 (4x-2)/9 = 5/3 ?

The solutions to the equation (2x+3)/6 (4x-2)/9 = 5/3 are x=3,x=-4

Find the zeros of (2x+3)/6 (4x-2)/9 = 5/3

The zeros of (2x+3)/6 (4x-2)/9 = 5/3 are x=3,x=-4

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\frac{2 x + 3}{6} \frac{4 x - 2}{9} = \frac{5}{3}

x = 3, x = - 4

Solution steps

\frac{2 x + 3}{6} \cdot \frac{4 x - 2}{9} = \frac{5}{3}

Simplify

6 \cdot 9 : 54

\frac{( 2 x + 3 ) ( 4 x - 2 )}{54} = \frac{5}{3}

Find Least Common Multiplier of

54, 3 : 54

Multiply by LCM=

54

\frac{( 2 x + 3 ) ( 4 x - 2 )}{54} \cdot 54 = \frac{5}{3} \cdot 54

Simplify

(2 x + 3) (4 x - 2) = 90

Expand

(2 x + 3) (4 x - 2) : 8 x^{2} + 8 x - 6

8 x^{2} + 8 x - 6 = 90

Move

90

to the left side

8 x^{2} + 8 x - 96 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 8 ( - 96 )}{2 \cdot 8}

8^{2} - 4 \cdot 8 (- 96) = 56

x_{1, 2} = \frac{- 8 \pm 56}{2 \cdot 8}

Separate the solutions

x_{1} = \frac{- 8 + 56}{2 \cdot 8}, x_{2} = \frac{- 8 - 56}{2 \cdot 8}

x = \frac{- 8 + 56}{2 \cdot 8} : 3

x = \frac{- 8 - 56}{2 \cdot 8} : - 4

The solutions to the quadratic equation are:

x = 3, x = - 4

12 x^{2} - 5 x + 2 = 0

80 = x (\frac{x}{10} - 3) - 5 (\frac{x}{10} - 3)^{2}

x, 4 x^{2} - 12 x + 9 = 0

10700 x^{2} + 5000 x + 3500 = 0

(x - 5) (x + 5) = (x - 1)

What are the solutions to the equation (2x+3)/6 (4x-2)/9 = 5/3 ?
The solutions to the equation (2x+3)/6 (4x-2)/9 = 5/3 are x=3,x=-4
Find the zeros of (2x+3)/6 (4x-2)/9 = 5/3
The zeros of (2x+3)/6 (4x-2)/9 = 5/3 are x=3,x=-4