Algebra Examples

$4 x (x + 1) = (2 x - 3) (2 x + 5)$

Step 1

Simplify $4 x (x + 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + 4 x (x + 1) = (2 x - 3) (2 x + 5)$

Step 1.2

Simplify by adding zeros.

$4 x (x + 1) = (2 x - 3) (2 x + 5)$

Step 1.3

Apply the distributive property.

$4 x \cdot x + 4 x \cdot 1 = (2 x - 3) (2 x + 5)$

Step 1.4

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

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Step 1.4.1

Move $x$ .

$4 (x \cdot x) + 4 x \cdot 1 = (2 x - 3) (2 x + 5)$

Step 1.4.2

Multiply $x$ by $x$ .

$4 x^{2} + 4 x \cdot 1 = (2 x - 3) (2 x + 5)$

Step 1.5

Multiply $4$ by $1$ .

$4 x^{2} + 4 x = (2 x - 3) (2 x + 5)$

Step 2

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

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

$4 x^{2} + 4 x = 2 x (2 x + 5) - 3 (2 x + 5)$

Step 2.1.2

Apply the distributive property.

$4 x^{2} + 4 x = 2 x (2 x) + 2 x \cdot 5 - 3 (2 x + 5)$

Step 2.1.3

Apply the distributive property.

$4 x^{2} + 4 x = 2 x (2 x) + 2 x \cdot 5 - 3 (2 x) - 3 \cdot 5$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Rewrite using the commutative property of multiplication.

$4 x^{2} + 4 x = 2 \cdot 2 x \cdot x + 2 x \cdot 5 - 3 (2 x) - 3 \cdot 5$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

$4 x^{2} + 4 x = 2 \cdot 2 (x \cdot x) + 2 x \cdot 5 - 3 (2 x) - 3 \cdot 5$

Step 2.2.1.2.2

Multiply $x$ by $x$ .

$4 x^{2} + 4 x = 2 \cdot 2 x^{2} + 2 x \cdot 5 - 3 (2 x) - 3 \cdot 5$

Step 2.2.1.3

Multiply $2$ by $2$ .

$4 x^{2} + 4 x = 4 x^{2} + 2 x \cdot 5 - 3 (2 x) - 3 \cdot 5$

Step 2.2.1.4

Multiply $5$ by $2$ .

$4 x^{2} + 4 x = 4 x^{2} + 10 x - 3 (2 x) - 3 \cdot 5$

Step 2.2.1.5

Multiply $2$ by $- 3$ .

$4 x^{2} + 4 x = 4 x^{2} + 10 x - 6 x - 3 \cdot 5$

Step 2.2.1.6

Multiply $- 3$ by $5$ .

$4 x^{2} + 4 x = 4 x^{2} + 10 x - 6 x - 15$

Step 2.2.2

Subtract $6 x$ from $10 x$ .

$4 x^{2} + 4 x = 4 x^{2} + 4 x - 15$

Step 3

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

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Step 3.1

Subtract $4 x^{2}$ from both sides of the equation.

$4 x^{2} + 4 x - 4 x^{2} = 4 x - 15$

Step 3.2

Subtract $4 x$ from both sides of the equation.

$4 x^{2} + 4 x - 4 x^{2} - 4 x = - 15$

Step 3.3

Combine the opposite terms in $4 x^{2} + 4 x - 4 x^{2} - 4 x$ .

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Step 3.3.1

Subtract $4 x^{2}$ from $4 x^{2}$ .

$4 x + 0 - 4 x = - 15$

Step 3.3.2

Add $4 x$ and $0$ .

$4 x - 4 x = - 15$

Step 3.3.3

Subtract $4 x$ from $4 x$ .

$0 = - 15$

Step 4

Since $0 \neq - 15$ , there are no solutions.

No solution