Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $3$ by $2$ .

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

Step 1.3

Rewrite using the commutative property of multiplication.

$6 x + 2 \cdot - 2 x \cdot x + 1 = 6 x^{2} - 4 x + 1$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $x$ .

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

Step 1.4.1.2

Multiply $x$ by $x$ .

$6 x + 2 \cdot - 2 x^{2} + 1 = 6 x^{2} - 4 x + 1$

Step 1.4.2

Multiply $2$ by $- 2$ .

$6 x - 4 x^{2} + 1 = 6 x^{2} - 4 x + 1$

Step 2

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

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Step 2.1

Subtract $6 x^{2}$ from both sides of the equation.

$6 x - 4 x^{2} + 1 - 6 x^{2} = - 4 x + 1$

Step 2.2

Add $4 x$ to both sides of the equation.

$6 x - 4 x^{2} + 1 - 6 x^{2} + 4 x = 1$

Step 2.3

Add $6 x$ and $4 x$ .

$- 4 x^{2} + 1 - 6 x^{2} + 10 x = 1$

Step 2.4

Subtract $6 x^{2}$ from $- 4 x^{2}$ .

$- 10 x^{2} + 1 + 10 x = 1$

Step 3

Subtract $1$ from both sides of the equation.

$- 10 x^{2} + 1 + 10 x - 1 = 0$

Step 4

Combine the opposite terms in $- 10 x^{2} + 1 + 10 x - 1$ .

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Step 4.1

Subtract $1$ from $1$ .

$- 10 x^{2} + 10 x + 0 = 0$

Step 4.2

Add $- 10 x^{2} + 10 x$ and $0$ .

$- 10 x^{2} + 10 x = 0$

Step 5

Factor $- 10 x$ out of $- 10 x^{2} + 10 x$ .

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Step 5.1

Factor $- 10 x$ out of $- 10 x^{2}$ .

$- 10 x \cdot x + 10 x = 0$

Step 5.2

Factor $- 10 x$ out of $10 x$ .

$- 10 x \cdot x - 10 x \cdot - 1 = 0$

Step 5.3

Factor $- 10 x$ out of $- 10 x (x) - 10 x (- 1)$ .

$- 10 x (x - 1) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 1 = 0$

Step 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 8.2

Add $1$ to both sides of the equation.

$x = 1$

Step 9

The final solution is all the values that make $- 10 x (x - 1) = 0$ true.

$x = 0, 1$