Algebra Examples

$(2 w + 5) (3 w - 4) = 6$

Step 1

Subtract $6$ from both sides of the equation.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Apply the distributive property.

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

Step 2.1.1.3

Apply the distributive property.

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

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.

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

Step 2.1.2.1.2

Multiply $w$ by $w$ by adding the exponents.

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Step 2.1.2.1.2.1

Move $w$ .

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

Step 2.1.2.1.2.2

Multiply $w$ by $w$ .

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

Step 2.1.2.1.3

Multiply $2$ by $3$ .

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

Step 2.1.2.1.4

Multiply $- 4$ by $2$ .

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

Step 2.1.2.1.5

Multiply $3$ by $5$ .

$6 w^{2} - 8 w + 15 w + 5 \cdot - 4 - 6 = 0$

Step 2.1.2.1.6

Multiply $5$ by $- 4$ .

$6 w^{2} - 8 w + 15 w - 20 - 6 = 0$

Step 2.1.2.2

Add $- 8 w$ and $15 w$ .

$6 w^{2} + 7 w - 20 - 6 = 0$

Step 2.2

Subtract $6$ from $- 20$ .

$6 w^{2} + 7 w - 26 = 0$

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 $6 w^{2} + 7 w - 26$ .

$6 w^{2} + 7 w - 26 = 0$

Step 5