Solve (1-4x)(1-3x)5

Question

Simplify the expression

5 - 35 x + 60 x^{2}

Evaluate

(1 - 4 x) (1 - 3 x) \times 5

Use the commutative property to reorder the terms

5 (1 - 4 x) (1 - 3 x)

Multiply the terms

More Steps

Evaluate

5 (1 - 4 x)

Apply the distributive property

5 \times 1 - 5 \times 4 x

Any expression multiplied by 1 remains the same

5 - 5 \times 4 x

Multiply the numbers

5 - 20 x

(5 - 20 x) (1 - 3 x)

Apply the distributive property

5 \times 1 - 5 \times 3 x - 20 x \times 1 - (- 20 x \times 3 x)

Any expression multiplied by 1 remains the same

5 - 5 \times 3 x - 20 x \times 1 - (- 20 x \times 3 x)

Multiply the numbers

5 - 15 x - 20 x \times 1 - (- 20 x \times 3 x)

Any expression multiplied by 1 remains the same

5 - 15 x - 20 x - (- 20 x \times 3 x)

Multiply the terms

More Steps

Evaluate

- 20 x \times 3 x

Multiply the numbers

- 60 x \times x

Multiply the terms

- 60 x^{2}

5 - 15 x - 20 x - (- 60 x^{2})

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

5 - 15 x - 20 x + 60 x^{2}

Solution

More Steps

Evaluate

- 15 x - 20 x

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

(- 15 - 20) x

Subtract the numbers

- 35 x

5 - 35 x + 60 x^{2}

Show Solution

Find the roots

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

Alternative Form

x_{1} = 0.25, x_{2} = 0. \dot{3}

Evaluate

(1 - 4 x) (1 - 3 x) \times 5

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

(1 - 4 x) (1 - 3 x) \times 5 = 0

Use the commutative property to reorder the terms

5 (1 - 4 x) (1 - 3 x) = 0

Elimination the left coefficient

(1 - 4 x) (1 - 3 x) = 0

Separate the equation into 2 possible cases

1 - 4 x = 0 1 - 3 x = 0

Solve the equation

More Steps

Evaluate

1 - 4 x = 0

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

- 4 x = 0 - 1

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

- 4 x = - 1

Change the signs on both sides of the equation

4 x = 1

Divide both sides

\frac{4 x}{4} = \frac{1}{4}

Divide the numbers

x = \frac{1}{4}

x = \frac{1}{4} 1 - 3 x = 0

Solve the equation

More Steps

Evaluate

1 - 3 x = 0

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

- 3 x = 0 - 1

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

- 3 x = - 1

Change the signs on both sides of the equation

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = \frac{1}{4} x = \frac{1}{3}

Solution

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

Alternative Form

x_{1} = 0.25, x_{2} = 0. \dot{3}

Show Solution