Solve for x 8x(2x^3+3x-1)-4x^2(4x^2+6)+8=32

$8 x (2 x^{3} + 3 x - 1) - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Step 1

Simplify $8 x (2 x^{3} + 3 x - 1) - 4 x^{2} (4 x^{2} + 6) + 8$ .

Simplify each term.

Apply the distributive property.

$8 x (2 x^{3}) + 8 x (3 x) + 8 x \cdot - 1 - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Simplify.

Rewrite using the commutative property of multiplication.

$8 \cdot 2 x \cdot x^{3} + 8 x (3 x) + 8 x \cdot - 1 - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Rewrite using the commutative property of multiplication.

$8 \cdot 2 x \cdot x^{3} + 8 \cdot 3 x \cdot x + 8 x \cdot - 1 - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Multiply $- 1$ by $8$ .

$8 \cdot 2 x \cdot x^{3} + 8 \cdot 3 x \cdot x - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Simplify each term.

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$8 \cdot 2 (x^{3} x) + 8 \cdot 3 x \cdot x - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Multiply $x^{3}$ by $x$ .

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

$8 \cdot 2 (x^{3} x^{1}) + 8 \cdot 3 x \cdot x - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

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

$8 \cdot 2 x^{3 + 1} + 8 \cdot 3 x \cdot x - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Add $3$ and $1$ .

$8 \cdot 2 x^{4} + 8 \cdot 3 x \cdot x - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Multiply $8$ by $2$ .

$16 x^{4} + 8 \cdot 3 x \cdot x - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

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

Move $x$ .

$16 x^{4} + 8 \cdot 3 (x \cdot x) - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Multiply $x$ by $x$ .

$16 x^{4} + 8 \cdot 3 x^{2} - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Multiply $8$ by $3$ .

$16 x^{4} + 24 x^{2} - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Apply the distributive property.

$16 x^{4} + 24 x^{2} - 8 x - 4 x^{2} (4 x^{2}) - 4 x^{2} \cdot 6 + 8 = 32$

Rewrite using the commutative property of multiplication.

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 x^{2} x^{2} - 4 x^{2} \cdot 6 + 8 = 32$

Multiply $6$ by $- 4$ .

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 x^{2} x^{2} - 24 x^{2} + 8 = 32$

Simplify each term.

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

Move $x^{2}$ .

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 (x^{2} x^{2}) - 24 x^{2} + 8 = 32$

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

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 x^{2 + 2} - 24 x^{2} + 8 = 32$

Add $2$ and $2$ .

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 x^{4} - 24 x^{2} + 8 = 32$

Multiply $- 4$ by $4$ .

$16 x^{4} + 24 x^{2} - 8 x - 16 x^{4} - 24 x^{2} + 8 = 32$

Combine the opposite terms in $16 x^{4} + 24 x^{2} - 8 x - 16 x^{4} - 24 x^{2} + 8$ .

Subtract $16 x^{4}$ from $16 x^{4}$ .

$24 x^{2} - 8 x + 0 - 24 x^{2} + 8 = 32$

Add $24 x^{2} - 8 x$ and $0$ .

$24 x^{2} - 8 x - 24 x^{2} + 8 = 32$

Subtract $24 x^{2}$ from $24 x^{2}$ .

$- 8 x + 0 + 8 = 32$

Add $- 8 x$ and $0$ .

$- 8 x + 8 = 32$

Step 2

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

Subtract $8$ from both sides of the equation.

$- 8 x = 32 - 8$

Subtract $8$ from $32$ .

$- 8 x = 24$

Step 3

Divide each term in $- 8 x = 24$ by $- 8$ and simplify.

Divide each term in $- 8 x = 24$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{24}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{24}{- 8}$

Divide $x$ by $1$ .

$x = \frac{24}{- 8}$

Simplify the right side.

Divide $24$ by $- 8$ .

$x = - 3$

Solve for x 8x(2x^3+3x-1)-4x^2(4x^2+6)+8=32

Related Questions

Support LCMGCF.com by disabling your adblocker.