Algebra Examples

$2 x (x - 7) = 3 x (x - 8) + 1$

Step 1

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

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Step 1.1

Subtract $3 x (x - 8)$ from both sides of the equation.

$2 x (x - 7) - 3 x (x - 8) = 1$

Step 1.2

Subtract $1$ from both sides of the equation.

$2 x (x - 7) - 3 x (x - 8) - 1 = 0$

Step 2

Simplify $2 x (x - 7) - 3 x (x - 8) - 1$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 7 - 3 x (x - 8) - 1 = 0$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 7 - 3 x (x - 8) - 1 = 0$

Step 2.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 7 - 3 x (x - 8) - 1 = 0$

Step 2.1.3

Multiply $- 7$ by $2$ .

$2 x^{2} - 14 x - 3 x (x - 8) - 1 = 0$

Step 2.1.4

Apply the distributive property.

$2 x^{2} - 14 x - 3 x \cdot x - 3 x \cdot - 8 - 1 = 0$

Step 2.1.5

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

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Step 2.1.5.1

Move $x$ .

$2 x^{2} - 14 x - 3 (x \cdot x) - 3 x \cdot - 8 - 1 = 0$

Step 2.1.5.2

Multiply $x$ by $x$ .

$2 x^{2} - 14 x - 3 x^{2} - 3 x \cdot - 8 - 1 = 0$

Step 2.1.6

Multiply $- 8$ by $- 3$ .

$2 x^{2} - 14 x - 3 x^{2} + 24 x - 1 = 0$

Step 2.2

Subtract $3 x^{2}$ from $2 x^{2}$ .

$- x^{2} - 14 x + 24 x - 1 = 0$

Step 2.3

Add $- 14 x$ and $24 x$ .

$- x^{2} + 10 x - 1 = 0$

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 $- x^{2} + 10 x - 1$ .

$- x^{2} + 10 x - 1 = 0$

Step 5