Solve (4j-3)(2j-3)

Question

Simplify the expression

8 j^{2} - 18 j + 9

Evaluate

(4 j - 3) (2 j - 3)

Apply the distributive property

4 j \times 2 j - 4 j \times 3 - 3 \times 2 j - (- 3 \times 3)

Multiply the terms

More Steps

Evaluate

4 j \times 2 j

Multiply the numbers

8 j \times j

Multiply the terms

8 j^{2}

8 j^{2} - 4 j \times 3 - 3 \times 2 j - (- 3 \times 3)

Multiply the numbers

8 j^{2} - 12 j - 3 \times 2 j - (- 3 \times 3)

Multiply the numbers

8 j^{2} - 12 j - 6 j - (- 3 \times 3)

Multiply the numbers

8 j^{2} - 12 j - 6 j - (- 9)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

8 j^{2} - 12 j - 6 j + 9

Solution

More Steps

Evaluate

- 12 j - 6 j

Collect like terms by calculating the sum or difference of their coefficients

(- 12 - 6) j

Subtract the numbers

- 18 j

8 j^{2} - 18 j + 9

Show Solution

Find the roots

j_{1} = \frac{3}{4}, j_{2} = \frac{3}{2}

Alternative Form

j_{1} = 0.75, j_{2} = 1.5

Evaluate

(4 j - 3) (2 j - 3)

To find the roots of the expression,set the expression equal to 0

(4 j - 3) (2 j - 3) = 0

Separate the equation into 2 possible cases

4 j - 3 = 0 2 j - 3 = 0

Solve the equation

More Steps

Evaluate

4 j - 3 = 0

Move the constant to the right-hand side and change its sign

4 j = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

4 j = 3

Divide both sides

\frac{4 j}{4} = \frac{3}{4}

Divide the numbers

j = \frac{3}{4}

j = \frac{3}{4} 2 j - 3 = 0

Solve the equation

More Steps

Evaluate

2 j - 3 = 0

Move the constant to the right-hand side and change its sign

2 j = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

2 j = 3

Divide both sides

\frac{2 j}{2} = \frac{3}{2}

Divide the numbers

j = \frac{3}{2}

j = \frac{3}{4} j = \frac{3}{2}

Solution

j_{1} = \frac{3}{4}, j_{2} = \frac{3}{2}

Alternative Form

j_{1} = 0.75, j_{2} = 1.5

Show Solution