Algebra Examples

$(2 x - 3) (4 x - 5) = - 6$

Step 1

Add $6$ to both sides of the equation.

$(2 x - 3) (4 x - 5) + 6 = 0$

Step 2

Simplify $(2 x - 3) (4 x - 5) + 6$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $(2 x - 3) (4 x - 5)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

$2 x (4 x - 5) - 3 (4 x - 5) + 6 = 0$

Step 2.1.1.2

Apply the distributive property.

$2 x (4 x) + 2 x \cdot - 5 - 3 (4 x - 5) + 6 = 0$

Step 2.1.1.3

Apply the distributive property.

$2 x (4 x) + 2 x \cdot - 5 - 3 (4 x) - 3 \cdot - 5 + 6 = 0$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 4 x \cdot x + 2 x \cdot - 5 - 3 (4 x) - 3 \cdot - 5 + 6 = 0$

Step 2.1.2.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.2.1.2.1

Move $x$ .

$2 \cdot 4 (x \cdot x) + 2 x \cdot - 5 - 3 (4 x) - 3 \cdot - 5 + 6 = 0$

Step 2.1.2.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 4 x^{2} + 2 x \cdot - 5 - 3 (4 x) - 3 \cdot - 5 + 6 = 0$

Step 2.1.2.1.3

Multiply $2$ by $4$ .

$8 x^{2} + 2 x \cdot - 5 - 3 (4 x) - 3 \cdot - 5 + 6 = 0$

Step 2.1.2.1.4

Multiply $- 5$ by $2$ .

$8 x^{2} - 10 x - 3 (4 x) - 3 \cdot - 5 + 6 = 0$

Step 2.1.2.1.5

Multiply $4$ by $- 3$ .

$8 x^{2} - 10 x - 12 x - 3 \cdot - 5 + 6 = 0$

Step 2.1.2.1.6

Multiply $- 3$ by $- 5$ .

$8 x^{2} - 10 x - 12 x + 15 + 6 = 0$

Step 2.1.2.2

Subtract $12 x$ from $- 10 x$ .

$8 x^{2} - 22 x + 15 + 6 = 0$

Step 2.2

Add $15$ and $6$ .

$8 x^{2} - 22 x + 21 = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $8 x^{2} - 22 x + 21$ .

$8 x^{2} - 22 x + 21 = 0$

Step 5