Algebra Examples

$8 x^{2} (2 x - 7) - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1

Simplify $8 x^{2} (2 x - 7) - 4 x (4 x^{2} - 5 x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 x^{2} (2 x) + 8 x^{2} \cdot - 7 - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$8 \cdot 2 x^{2} x + 8 x^{2} \cdot - 7 - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.3

Multiply $- 7$ by $8$ .

$8 \cdot 2 x^{2} x - 56 x^{2} - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

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

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Step 1.1.4.1.1

Move $x$ .

$8 \cdot 2 (x \cdot x^{2}) - 56 x^{2} - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.4.1.2

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

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Step 1.1.4.1.2.1

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

$8 \cdot 2 (x^{1} x^{2}) - 56 x^{2} - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.4.1.2.2

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

$8 \cdot 2 x^{1 + 2} - 56 x^{2} - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.4.1.3

Add $1$ and $2$ .

$8 \cdot 2 x^{3} - 56 x^{2} - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.4.2

Multiply $8$ by $2$ .

$16 x^{3} - 56 x^{2} - 4 x (4 x^{2} - 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.5

Apply the distributive property.

$16 x^{3} - 56 x^{2} - 4 x (4 x^{2}) - 4 x (- 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.6

Rewrite using the commutative property of multiplication.

$16 x^{3} - 56 x^{2} - 4 \cdot 4 x \cdot x^{2} - 4 x (- 5 x) = - 6 x (6 x + 5) + 90$

Step 1.1.7

Rewrite using the commutative property of multiplication.

$16 x^{3} - 56 x^{2} - 4 \cdot 4 x \cdot x^{2} - 4 \cdot - 5 x \cdot x = - 6 x (6 x + 5) + 90$

Step 1.1.8

Simplify each term.

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Step 1.1.8.1

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

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Step 1.1.8.1.1

Move $x^{2}$ .

$16 x^{3} - 56 x^{2} - 4 \cdot 4 (x^{2} x) - 4 \cdot - 5 x \cdot x = - 6 x (6 x + 5) + 90$

Step 1.1.8.1.2

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

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Step 1.1.8.1.2.1

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

$16 x^{3} - 56 x^{2} - 4 \cdot 4 (x^{2} x^{1}) - 4 \cdot - 5 x \cdot x = - 6 x (6 x + 5) + 90$

Step 1.1.8.1.2.2

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

$16 x^{3} - 56 x^{2} - 4 \cdot 4 x^{2 + 1} - 4 \cdot - 5 x \cdot x = - 6 x (6 x + 5) + 90$

Step 1.1.8.1.3

Add $2$ and $1$ .

$16 x^{3} - 56 x^{2} - 4 \cdot 4 x^{3} - 4 \cdot - 5 x \cdot x = - 6 x (6 x + 5) + 90$

Step 1.1.8.2

Multiply $- 4$ by $4$ .

$16 x^{3} - 56 x^{2} - 16 x^{3} - 4 \cdot - 5 x \cdot x = - 6 x (6 x + 5) + 90$

Step 1.1.8.3

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

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Step 1.1.8.3.1

Move $x$ .

$16 x^{3} - 56 x^{2} - 16 x^{3} - 4 \cdot - 5 (x \cdot x) = - 6 x (6 x + 5) + 90$

Step 1.1.8.3.2

Multiply $x$ by $x$ .

$16 x^{3} - 56 x^{2} - 16 x^{3} - 4 \cdot - 5 x^{2} = - 6 x (6 x + 5) + 90$

Step 1.1.8.4

Multiply $- 4$ by $- 5$ .

$16 x^{3} - 56 x^{2} - 16 x^{3} + 20 x^{2} = - 6 x (6 x + 5) + 90$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $16 x^{3} - 56 x^{2} - 16 x^{3} + 20 x^{2}$ .

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Step 1.2.1.1

Subtract $16 x^{3}$ from $16 x^{3}$ .

$- 56 x^{2} + 0 + 20 x^{2} = - 6 x (6 x + 5) + 90$

Step 1.2.1.2

Add $- 56 x^{2}$ and $0$ .

$- 56 x^{2} + 20 x^{2} = - 6 x (6 x + 5) + 90$

Step 1.2.2

Add $- 56 x^{2}$ and $20 x^{2}$ .

$- 36 x^{2} = - 6 x (6 x + 5) + 90$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$- 36 x^{2} = - 6 x (6 x) - 6 x \cdot 5 + 90$

Step 2.2

Rewrite using the commutative property of multiplication.

$- 36 x^{2} = - 6 \cdot 6 x \cdot x - 6 x \cdot 5 + 90$

Step 2.3

Multiply $5$ by $- 6$ .

$- 36 x^{2} = - 6 \cdot 6 x \cdot x - 30 x + 90$

Step 2.4

Simplify each term.

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Step 2.4.1

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

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Step 2.4.1.1

Move $x$ .

$- 36 x^{2} = - 6 \cdot 6 (x \cdot x) - 30 x + 90$

Step 2.4.1.2

Multiply $x$ by $x$ .

$- 36 x^{2} = - 6 \cdot 6 x^{2} - 30 x + 90$

Step 2.4.2

Multiply $- 6$ by $6$ .

$- 36 x^{2} = - 36 x^{2} - 30 x + 90$

Step 3

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 36 x^{2} - 30 x + 90 = - 36 x^{2}$

Step 4

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

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Step 4.1

Add $36 x^{2}$ to both sides of the equation.

$- 36 x^{2} - 30 x + 90 + 36 x^{2} = 0$

Step 4.2

Combine the opposite terms in $- 36 x^{2} - 30 x + 90 + 36 x^{2}$ .

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Step 4.2.1

Add $- 36 x^{2}$ and $36 x^{2}$ .

$- 30 x + 90 + 0 = 0$

Step 4.2.2

Add $- 30 x + 90$ and $0$ .

$- 30 x + 90 = 0$

Step 5

Subtract $90$ from both sides of the equation.

$- 30 x = - 90$

Step 6

Divide each term in $- 30 x = - 90$ by $- 30$ and simplify.

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Step 6.1

Divide each term in $- 30 x = - 90$ by $- 30$ .

$\frac{- 30 x}{- 30} = \frac{- 90}{- 30}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 30$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 30 x}{- 30} = \frac{- 90}{- 30}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 90}{- 30}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 90$ by $- 30$ .

$x = 3$