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

Question

Simplify the expression

1 - 7 x + 12 x^{2}

Evaluate

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

Apply the distributive property

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Evaluate

- 4 x \times 3 x

Multiply the numbers

- 12 x \times x

Multiply the terms

- 12 x^{2}

1 - 3 x - 4 x - (- 12 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

1 - 3 x - 4 x + 12 x^{2}

Solution

More Steps

Evaluate

- 3 x - 4 x

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

(- 3 - 4) x

Subtract the numbers

- 7 x

1 - 7 x + 12 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)

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

(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