Pre-Algebra Examples

$(x - 8) (5 x - 6) = (x - 6) (7 x - 6)$

Step 1

Simplify $(x - 8) (5 x - 6)$ .

Tap for more steps...

Step 1.1

Expand $(x - 8) (5 x - 6)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$x (5 x - 6) - 8 (5 x - 6) = (x - 6) (7 x - 6)$

Step 1.1.2

Apply the distributive property.

$x (5 x) + x \cdot - 6 - 8 (5 x - 6) = (x - 6) (7 x - 6)$

Step 1.1.3

Apply the distributive property.

$x (5 x) + x \cdot - 6 - 8 (5 x) - 8 \cdot - 6 = (x - 6) (7 x - 6)$

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$5 x \cdot x + x \cdot - 6 - 8 (5 x) - 8 \cdot - 6 = (x - 6) (7 x - 6)$

Step 1.2.1.2

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

Tap for more steps...

Step 1.2.1.2.1

Move $x$ .

$5 (x \cdot x) + x \cdot - 6 - 8 (5 x) - 8 \cdot - 6 = (x - 6) (7 x - 6)$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

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

Step 1.2.1.3

Move $- 6$ to the left of $x$ .

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

Step 1.2.1.4

Multiply $5$ by $- 8$ .

$5 x^{2} - 6 x - 40 x - 8 \cdot - 6 = (x - 6) (7 x - 6)$

Step 1.2.1.5

Multiply $- 8$ by $- 6$ .

$5 x^{2} - 6 x - 40 x + 48 = (x - 6) (7 x - 6)$

Step 1.2.2

Subtract $40 x$ from $- 6 x$ .

$5 x^{2} - 46 x + 48 = (x - 6) (7 x - 6)$

Step 2

Simplify $(x - 6) (7 x - 6)$ .

Tap for more steps...

Step 2.1

Expand $(x - 6) (7 x - 6)$ using the FOIL Method.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$5 x^{2} - 46 x + 48 = x (7 x - 6) - 6 (7 x - 6)$

Step 2.1.2

Apply the distributive property.

$5 x^{2} - 46 x + 48 = x (7 x) + x \cdot - 6 - 6 (7 x - 6)$

Step 2.1.3

Apply the distributive property.

$5 x^{2} - 46 x + 48 = x (7 x) + x \cdot - 6 - 6 (7 x) - 6 \cdot - 6$

Step 2.2

Simplify and combine like terms.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

Rewrite using the commutative property of multiplication.

$5 x^{2} - 46 x + 48 = 7 x \cdot x + x \cdot - 6 - 6 (7 x) - 6 \cdot - 6$

Step 2.2.1.2

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

Tap for more steps...

Step 2.2.1.2.1

Move $x$ .

$5 x^{2} - 46 x + 48 = 7 (x \cdot x) + x \cdot - 6 - 6 (7 x) - 6 \cdot - 6$

Step 2.2.1.2.2

Multiply $x$ by $x$ .

$5 x^{2} - 46 x + 48 = 7 x^{2} + x \cdot - 6 - 6 (7 x) - 6 \cdot - 6$

Step 2.2.1.3

Move $- 6$ to the left of $x$ .

$5 x^{2} - 46 x + 48 = 7 x^{2} - 6 \cdot x - 6 (7 x) - 6 \cdot - 6$

Step 2.2.1.4

Multiply $7$ by $- 6$ .

$5 x^{2} - 46 x + 48 = 7 x^{2} - 6 x - 42 x - 6 \cdot - 6$

Step 2.2.1.5

Multiply $- 6$ by $- 6$ .

$5 x^{2} - 46 x + 48 = 7 x^{2} - 6 x - 42 x + 36$

Step 2.2.2

Subtract $42 x$ from $- 6 x$ .

$5 x^{2} - 46 x + 48 = 7 x^{2} - 48 x + 36$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 2, 3$

Step 4