Algebra Examples

$7 x (4 x^{2} + 6) = 4 (7 x^{3} + 9 x - 12)$

Step 1

Simplify $7 x (4 x^{2} + 6)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + 7 x (4 x^{2} + 6) = 4 (7 x^{3} + 9 x - 12)$

Step 1.2

Simplify by multiplying through.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$7 x (4 x^{2}) + 7 x \cdot 6 = 4 (7 x^{3} + 9 x - 12)$

Step 1.2.2

Simplify the expression.

Tap for more steps...

Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$7 \cdot 4 x \cdot x^{2} + 7 x \cdot 6 = 4 (7 x^{3} + 9 x - 12)$

Step 1.2.2.2

Multiply $6$ by $7$ .

$7 \cdot 4 x \cdot x^{2} + 42 x = 4 (7 x^{3} + 9 x - 12)$

Step 1.3

Simplify each term.

Tap for more steps...

Step 1.3.1

Multiply $x$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 1.3.1.1

Move $x^{2}$ .

$7 \cdot 4 (x^{2} x) + 42 x = 4 (7 x^{3} + 9 x - 12)$

Step 1.3.1.2

Multiply $x^{2}$ by $x$ .

Tap for more steps...

Step 1.3.1.2.1

Raise $x$ to the power of $1$ .

$7 \cdot 4 (x^{2} x^{1}) + 42 x = 4 (7 x^{3} + 9 x - 12)$

Step 1.3.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 \cdot 4 x^{2 + 1} + 42 x = 4 (7 x^{3} + 9 x - 12)$

Step 1.3.1.3

Add $2$ and $1$ .

$7 \cdot 4 x^{3} + 42 x = 4 (7 x^{3} + 9 x - 12)$

Step 1.3.2

Multiply $7$ by $4$ .

$28 x^{3} + 42 x = 4 (7 x^{3} + 9 x - 12)$

Step 2

Simplify $4 (7 x^{3} + 9 x - 12)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

$28 x^{3} + 42 x = 4 (7 x^{3}) + 4 (9 x) + 4 \cdot - 12$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Multiply $7$ by $4$ .

$28 x^{3} + 42 x = 28 x^{3} + 4 (9 x) + 4 \cdot - 12$

Step 2.2.2

Multiply $9$ by $4$ .

$28 x^{3} + 42 x = 28 x^{3} + 36 x + 4 \cdot - 12$

Step 2.2.3

Multiply $4$ by $- 12$ .

$28 x^{3} + 42 x = 28 x^{3} + 36 x - 48$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $28 x^{3}$ from both sides of the equation.

$28 x^{3} + 42 x - 28 x^{3} = 36 x - 48$

Step 3.2

Subtract $36 x$ from both sides of the equation.

$28 x^{3} + 42 x - 28 x^{3} - 36 x = - 48$

Step 3.3

Combine the opposite terms in $28 x^{3} + 42 x - 28 x^{3} - 36 x$ .

Tap for more steps...

Step 3.3.1

Subtract $28 x^{3}$ from $28 x^{3}$ .

$42 x + 0 - 36 x = - 48$

Step 3.3.2

Add $42 x$ and $0$ .

$42 x - 36 x = - 48$

Step 3.4

Subtract $36 x$ from $42 x$ .

$6 x = - 48$

Step 4

Divide each term in $6 x = - 48$ by $6$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $6 x = - 48$ by $6$ .

$\frac{6 x}{6} = \frac{- 48}{6}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 48}{6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 48}{6}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $- 48$ by $6$ .

$x = - 8$