Pre-Algebra Examples

$x (4 x - 1) = 3 x$

Step 1

Simplify $x (4 x - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + x (4 x - 1) = 3 x$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$x (4 x) + x \cdot - 1 = 3 x$

Step 1.2.2

Reorder.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$4 x \cdot x + x \cdot - 1 = 3 x$

Step 1.2.2.2

Move $- 1$ to the left of $x$ .

$4 x \cdot x - 1 \cdot x = 3 x$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $x$ .

$4 (x \cdot x) - 1 \cdot x = 3 x$

Step 1.3.1.2

Multiply $x$ by $x$ .

$4 x^{2} - 1 \cdot x = 3 x$

Step 1.3.2

Rewrite $- 1 x$ as $- x$ .

$4 x^{2} - x = 3 x$

Step 2

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

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Step 2.1

Subtract $3 x$ from both sides of the equation.

$4 x^{2} - x - 3 x = 0$

Step 2.2

Subtract $3 x$ from $- x$ .

$4 x^{2} - 4 x = 0$

Step 3

Factor $4 x$ out of $4 x^{2} - 4 x$ .

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Step 3.1

Factor $4 x$ out of $4 x^{2}$ .

$4 x (x) - 4 x = 0$

Step 3.2

Factor $4 x$ out of $- 4 x$ .

$4 x (x) + 4 x (- 1) = 0$

Step 3.3

Factor $4 x$ out of $4 x (x) + 4 x (- 1)$ .

$4 x (x - 1) = 0$

Step 4

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 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

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

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Step 6.1

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

$x - 1 = 0$

Step 6.2

Add $1$ to both sides of the equation.

$x = 1$

Step 7

The final solution is all the values that make $4 x (x - 1) = 0$ true.

$x = 0, 1$