Pre-Algebra Examples

$(2 x - 4) (5 x + 4) = - 20$

Step 1

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

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

$2 x (5 x + 4) - 4 (5 x + 4) = - 20$

Step 1.1.2

Apply the distributive property.

$2 x (5 x) + 2 x \cdot 4 - 4 (5 x + 4) = - 20$

Step 1.1.3

Apply the distributive property.

$2 x (5 x) + 2 x \cdot 4 - 4 (5 x) - 4 \cdot 4 = - 20$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 5 x \cdot x + 2 x \cdot 4 - 4 (5 x) - 4 \cdot 4 = - 20$

Step 1.2.1.2

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

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Step 1.2.1.2.1

Move $x$ .

$2 \cdot 5 (x \cdot x) + 2 x \cdot 4 - 4 (5 x) - 4 \cdot 4 = - 20$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 5 x^{2} + 2 x \cdot 4 - 4 (5 x) - 4 \cdot 4 = - 20$

Step 1.2.1.3

Multiply $2$ by $5$ .

$10 x^{2} + 2 x \cdot 4 - 4 (5 x) - 4 \cdot 4 = - 20$

Step 1.2.1.4

Multiply $4$ by $2$ .

$10 x^{2} + 8 x - 4 (5 x) - 4 \cdot 4 = - 20$

Step 1.2.1.5

Multiply $5$ by $- 4$ .

$10 x^{2} + 8 x - 20 x - 4 \cdot 4 = - 20$

Step 1.2.1.6

Multiply $- 4$ by $4$ .

$10 x^{2} + 8 x - 20 x - 16 = - 20$

Step 1.2.2

Subtract $20 x$ from $8 x$ .

$10 x^{2} - 12 x - 16 = - 20$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 3