Solve (4-3x)(2x-3)

Question

Simplify the expression

17 x - 12 - 6 x^{2}

Evaluate

(4 - 3 x) (2 x - 3)

Apply the distributive property

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

Multiply the numbers

8 x - 4 \times 3 - 3 x \times 2 x - (- 3 x \times 3)

Multiply the numbers

8 x - 12 - 3 x \times 2 x - (- 3 x \times 3)

Multiply the terms

More Steps

Evaluate

- 3 x \times 2 x

Multiply the numbers

- 6 x \times x

Multiply the terms

- 6 x^{2}

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

Multiply the numbers

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

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 x - 12 - 6 x^{2} + 9 x

Solution

More Steps

Evaluate

8 x + 9 x

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

(8 + 9) x

Add the numbers

17 x

17 x - 12 - 6 x^{2}

Show Solution

Find the roots

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

Alternative Form

x_{1} = 1. \dot{3}, x_{2} = 1.5

Evaluate

(4 - 3 x) (2 x - 3)

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

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

Separate the equation into 2 possible cases

4 - 3 x = 0 2 x - 3 = 0

Solve the equation

More Steps

Evaluate

4 - 3 x = 0

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

- 3 x = 0 - 4

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

- 3 x = - 4

Change the signs on both sides of the equation

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

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

Solve the equation

More Steps

Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

\frac{2 x}{2} = \frac{3}{2}

Divide the numbers

x = \frac{3}{2}

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

Solution

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

Alternative Form

x_{1} = 1. \dot{3}, x_{2} = 1.5

Show Solution