Finite Math Examples

$2 (x - 3) (x + 1) - (x - 2) (x + 4) = x (x - 7)$

Step 1

Simplify $2 (x - 3) (x + 1) - (x - 2) (x + 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$(2 x + 2 \cdot - 3) (x + 1) - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.2

Multiply $2$ by $- 3$ .

$(2 x - 6) (x + 1) - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.3

Expand $(2 x - 6) (x + 1)$ using the FOIL Method.

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Step 1.1.3.1

Apply the distributive property.

$2 x (x + 1) - 6 (x + 1) - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.3.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 1 - 6 (x + 1) - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.3.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 1 - 6 x - 6 \cdot 1 - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.4

Simplify and combine like terms.

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Step 1.1.4.1

Simplify each term.

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Step 1.1.4.1.1

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

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Step 1.1.4.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 1 - 6 x - 6 \cdot 1 - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.4.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 1 - 6 x - 6 \cdot 1 - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.4.1.2

Multiply $2$ by $1$ .

$2 x^{2} + 2 x - 6 x - 6 \cdot 1 - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.4.1.3

Multiply $- 6$ by $1$ .

$2 x^{2} + 2 x - 6 x - 6 - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.4.2

Subtract $6 x$ from $2 x$ .

$2 x^{2} - 4 x - 6 - (x - 2) (x + 4) = x (x - 7)$

Step 1.1.5

Apply the distributive property.

$2 x^{2} - 4 x - 6 + (- x - - 2) (x + 4) = x (x - 7)$

Step 1.1.6

Multiply $- 1$ by $- 2$ .

$2 x^{2} - 4 x - 6 + (- x + 2) (x + 4) = x (x - 7)$

Step 1.1.7

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

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Step 1.1.7.1

Apply the distributive property.

$2 x^{2} - 4 x - 6 - x (x + 4) + 2 (x + 4) = x (x - 7)$

Step 1.1.7.2

Apply the distributive property.

$2 x^{2} - 4 x - 6 - x \cdot x - x \cdot 4 + 2 (x + 4) = x (x - 7)$

Step 1.1.7.3

Apply the distributive property.

$2 x^{2} - 4 x - 6 - x \cdot x - x \cdot 4 + 2 x + 2 \cdot 4 = x (x - 7)$

Step 1.1.8

Simplify and combine like terms.

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Step 1.1.8.1

Simplify each term.

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Step 1.1.8.1.1

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

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Step 1.1.8.1.1.1

Move $x$ .

$2 x^{2} - 4 x - 6 - (x \cdot x) - x \cdot 4 + 2 x + 2 \cdot 4 = x (x - 7)$

Step 1.1.8.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} - 4 x - 6 - x^{2} - x \cdot 4 + 2 x + 2 \cdot 4 = x (x - 7)$

Step 1.1.8.1.2

Multiply $4$ by $- 1$ .

$2 x^{2} - 4 x - 6 - x^{2} - 4 x + 2 x + 2 \cdot 4 = x (x - 7)$

Step 1.1.8.1.3

Multiply $2$ by $4$ .

$2 x^{2} - 4 x - 6 - x^{2} - 4 x + 2 x + 8 = x (x - 7)$

Step 1.1.8.2

Add $- 4 x$ and $2 x$ .

$2 x^{2} - 4 x - 6 - x^{2} - 2 x + 8 = x (x - 7)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

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

$x^{2} - 4 x - 6 - 2 x + 8 = x (x - 7)$

Step 1.2.2

Subtract $2 x$ from $- 4 x$ .

$x^{2} - 6 x - 6 + 8 = x (x - 7)$

Step 1.2.3

Add $- 6$ and $8$ .

$x^{2} - 6 x + 2 = x (x - 7)$

Step 2

Simplify $x (x - 7)$ .

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Step 2.1

Apply the distributive property.

$x^{2} - 6 x + 2 = x \cdot x + x \cdot - 7$

Step 2.2

Simplify the expression.

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Step 2.2.1

Multiply $x$ by $x$ .

$x^{2} - 6 x + 2 = x^{2} + x \cdot - 7$

Step 2.2.2

Move $- 7$ to the left of $x$ .

$x^{2} - 6 x + 2 = x^{2} - 7 x$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $x^{2}$ from both sides of the equation.

$x^{2} - 6 x + 2 - x^{2} = - 7 x$

Step 3.2

Add $7 x$ to both sides of the equation.

$x^{2} - 6 x + 2 - x^{2} + 7 x = 0$

Step 3.3

Combine the opposite terms in $x^{2} - 6 x + 2 - x^{2} + 7 x$ .

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Step 3.3.1

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

$- 6 x + 2 + 0 + 7 x = 0$

Step 3.3.2

Add $- 6 x + 2$ and $0$ .

$- 6 x + 2 + 7 x = 0$

Step 3.4

Add $- 6 x$ and $7 x$ .

$x + 2 = 0$

Step 4

Subtract $2$ from both sides of the equation.

$x = - 2$