Solve (4x-5)(x-3)=30

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{3}{4}, x_{2} = 5

Alternative Form

x_{1} = - 0.75, x_{2} = 5

Evaluate

(4 x - 5) (x - 3) = 30

Expand the expression

More Steps

Evaluate

(4 x - 5) (x - 3)

Apply the distributive property

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

Multiply the terms

4 x^{2} - 4 x \times 3 - 5 x - (- 5 \times 3)

Multiply the numbers

4 x^{2} - 12 x - 5 x - (- 5 \times 3)

Multiply the numbers

4 x^{2} - 12 x - 5 x - (- 15)

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

4 x^{2} - 12 x - 5 x + 15

Subtract the terms

More Steps

Evaluate

- 12 x - 5 x

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

(- 12 - 5) x

Subtract the numbers

- 17 x

4 x^{2} - 17 x + 15

4 x^{2} - 17 x + 15 = 30

Move the expression to the left side

4 x^{2} - 17 x - 15 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 17 x - 15

Rewrite the expression

4 x^{2} + (3 - 20) x - 15

Calculate

4 x^{2} + 3 x - 20 x - 15

Rewrite the expression

x \times 4 x + x \times 3 - 5 \times 4 x - 5 \times 3

Factor out x from the expression

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

Factor out - 5 from the expression

x (4 x + 3) - 5 (4 x + 3)

Factor out 4 x + 3 from the expression

(x - 5) (4 x + 3)

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

When the product of factors equals 0,at least one factor is 0

x - 5 = 0 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 3 = 0

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

4 x = 0 - 3

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

4 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{3}{4}

x = 5 x = - \frac{3}{4}

Solution

x_{1} = - \frac{3}{4}, x_{2} = 5

Alternative Form

x_{1} = - 0.75, x_{2} = 5

Show Solution

Solve the quadratic equation

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