Algebra Examples

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

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $5$ from both sides of the equation.

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

Step 1.2

Subtract $2 x$ from both sides of the equation.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $(x + 6) (3 x - 2)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Apply the distributive property.

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

Step 2.1.1.3

Apply the distributive property.

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

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.

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

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 $x$ .

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

Step 2.1.2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.2.1.3

Move $- 2$ to the left of $x$ .

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

Step 2.1.2.1.4

Multiply $3$ by $6$ .

$3 x^{2} - 2 x + 18 x + 6 \cdot - 2 - 5 - 2 x = 0$

Step 2.1.2.1.5

Multiply $6$ by $- 2$ .

$3 x^{2} - 2 x + 18 x - 12 - 5 - 2 x = 0$

Step 2.1.2.2

Add $- 2 x$ and $18 x$ .

$3 x^{2} + 16 x - 12 - 5 - 2 x = 0$

Step 2.2

Subtract $2 x$ from $16 x$ .

$3 x^{2} + 14 x - 12 - 5 = 0$

Step 2.3

Subtract $5$ from $- 12$ .

$3 x^{2} + 14 x - 17 = 0$

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 $3 x^{2} + 14 x - 17$ .

$3 x^{2} + 14 x - 17 = 0$

Step 5