Algebra Examples

$(2 a + 1) \cdot (6 a - 2) = 3 a \cdot (4 a - 1) + 4$

Step 1

Simplify $(2 a + 1) \cdot (6 a - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + (2 a + 1) \cdot (6 a - 2) = 3 a \cdot (4 a - 1) + 4$

Step 1.2

Simplify by adding zeros.

$(2 a + 1) \cdot (6 a - 2) = 3 a \cdot (4 a - 1) + 4$

Step 1.3

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

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Step 1.3.1

Apply the distributive property.

$2 a (6 a - 2) + 1 (6 a - 2) = 3 a \cdot (4 a - 1) + 4$

Step 1.3.2

Apply the distributive property.

$2 a (6 a) + 2 a \cdot - 2 + 1 (6 a - 2) = 3 a \cdot (4 a - 1) + 4$

Step 1.3.3

Apply the distributive property.

$2 a (6 a) + 2 a \cdot - 2 + 1 (6 a) + 1 \cdot - 2 = 3 a \cdot (4 a - 1) + 4$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 6 a \cdot a + 2 a \cdot - 2 + 1 (6 a) + 1 \cdot - 2 = 3 a \cdot (4 a - 1) + 4$

Step 1.4.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 1.4.1.2.1

Move $a$ .

$2 \cdot 6 (a \cdot a) + 2 a \cdot - 2 + 1 (6 a) + 1 \cdot - 2 = 3 a \cdot (4 a - 1) + 4$

Step 1.4.1.2.2

Multiply $a$ by $a$ .

$2 \cdot 6 a^{2} + 2 a \cdot - 2 + 1 (6 a) + 1 \cdot - 2 = 3 a \cdot (4 a - 1) + 4$

Step 1.4.1.3

Multiply $2$ by $6$ .

$12 a^{2} + 2 a \cdot - 2 + 1 (6 a) + 1 \cdot - 2 = 3 a \cdot (4 a - 1) + 4$

Step 1.4.1.4

Multiply $- 2$ by $2$ .

$12 a^{2} - 4 a + 1 (6 a) + 1 \cdot - 2 = 3 a \cdot (4 a - 1) + 4$

Step 1.4.1.5

Multiply $6 a$ by $1$ .

$12 a^{2} - 4 a + 6 a + 1 \cdot - 2 = 3 a \cdot (4 a - 1) + 4$

Step 1.4.1.6

Multiply $- 2$ by $1$ .

$12 a^{2} - 4 a + 6 a - 2 = 3 a \cdot (4 a - 1) + 4$

Step 1.4.2

Add $- 4 a$ and $6 a$ .

$12 a^{2} + 2 a - 2 = 3 a \cdot (4 a - 1) + 4$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$12 a^{2} + 2 a - 2 = 3 a (4 a) + 3 a \cdot - 1 + 4$

Step 2.2

Rewrite using the commutative property of multiplication.

$12 a^{2} + 2 a - 2 = 3 \cdot 4 a \cdot a + 3 a \cdot - 1 + 4$

Step 2.3

Multiply $- 1$ by $3$ .

$12 a^{2} + 2 a - 2 = 3 \cdot 4 a \cdot a - 3 a + 4$

Step 2.4

Simplify each term.

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Step 2.4.1

Multiply $a$ by $a$ by adding the exponents.

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Step 2.4.1.1

Move $a$ .

$12 a^{2} + 2 a - 2 = 3 \cdot 4 (a \cdot a) - 3 a + 4$

Step 2.4.1.2

Multiply $a$ by $a$ .

$12 a^{2} + 2 a - 2 = 3 \cdot 4 a^{2} - 3 a + 4$

Step 2.4.2

Multiply $3$ by $4$ .

$12 a^{2} + 2 a - 2 = 12 a^{2} - 3 a + 4$

Step 3

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

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Step 3.1

Subtract $12 a^{2}$ from both sides of the equation.

$12 a^{2} + 2 a - 2 - 12 a^{2} = - 3 a + 4$

Step 3.2

Add $3 a$ to both sides of the equation.

$12 a^{2} + 2 a - 2 - 12 a^{2} + 3 a = 4$

Step 3.3

Combine the opposite terms in $12 a^{2} + 2 a - 2 - 12 a^{2} + 3 a$ .

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Step 3.3.1

Subtract $12 a^{2}$ from $12 a^{2}$ .

$2 a - 2 + 0 + 3 a = 4$

Step 3.3.2

Add $2 a - 2$ and $0$ .

$2 a - 2 + 3 a = 4$

Step 3.4

Add $2 a$ and $3 a$ .

$5 a - 2 = 4$

Step 4

Move all terms not containing $a$ to the right side of the equation.

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Step 4.1

Add $2$ to both sides of the equation.

$5 a = 4 + 2$

Step 4.2

Add $4$ and $2$ .

$5 a = 6$

Step 5

Divide each term in $5 a = 6$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 a = 6$ by $5$ .

$\frac{5 a}{5} = \frac{6}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 a}{5} = \frac{6}{5}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{6}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{6}{5}$

Decimal Form:

$a = 1.2$

Mixed Number Form:

$a = 1 \frac{1}{5}$