Algebra Examples

$(3 x - 3) (2 x + 1) - 2 x (3 x - 7.5) = 0$

Step 1

Simplify $(3 x - 3) (2 x + 1) - 2 x (3 x - 7.5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Expand $(3 x - 3) (2 x + 1)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$3 x (2 x + 1) - 3 (2 x + 1) - 2 x (3 x - 7.5) = 0$

Step 1.1.1.2

Apply the distributive property.

$3 x (2 x) + 3 x \cdot 1 - 3 (2 x + 1) - 2 x (3 x - 7.5) = 0$

Step 1.1.1.3

Apply the distributive property.

$3 x (2 x) + 3 x \cdot 1 - 3 (2 x) - 3 \cdot 1 - 2 x (3 x - 7.5) = 0$

Step 1.1.2

Simplify and combine like terms.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x + 3 x \cdot 1 - 3 (2 x) - 3 \cdot 1 - 2 x (3 x - 7.5) = 0$

Step 1.1.2.1.2

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

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Step 1.1.2.1.2.1

Move $x$ .

$3 \cdot 2 (x \cdot x) + 3 x \cdot 1 - 3 (2 x) - 3 \cdot 1 - 2 x (3 x - 7.5) = 0$

Step 1.1.2.1.2.2

Multiply $x$ by $x$ .

$3 \cdot 2 x^{2} + 3 x \cdot 1 - 3 (2 x) - 3 \cdot 1 - 2 x (3 x - 7.5) = 0$

Step 1.1.2.1.3

Multiply $3$ by $2$ .

$6 x^{2} + 3 x \cdot 1 - 3 (2 x) - 3 \cdot 1 - 2 x (3 x - 7.5) = 0$

Step 1.1.2.1.4

Multiply $3$ by $1$ .

$6 x^{2} + 3 x - 3 (2 x) - 3 \cdot 1 - 2 x (3 x - 7.5) = 0$

Step 1.1.2.1.5

Multiply $2$ by $- 3$ .

$6 x^{2} + 3 x - 6 x - 3 \cdot 1 - 2 x (3 x - 7.5) = 0$

Step 1.1.2.1.6

Multiply $- 3$ by $1$ .

$6 x^{2} + 3 x - 6 x - 3 - 2 x (3 x - 7.5) = 0$

Step 1.1.2.2

Subtract $6 x$ from $3 x$ .

$6 x^{2} - 3 x - 3 - 2 x (3 x - 7.5) = 0$

Step 1.1.3

Apply the distributive property.

$6 x^{2} - 3 x - 3 - 2 x (3 x) - 2 x \cdot - 7.5 = 0$

Step 1.1.4

Rewrite using the commutative property of multiplication.

$6 x^{2} - 3 x - 3 - 2 \cdot 3 x \cdot x - 2 x \cdot - 7.5 = 0$

Step 1.1.5

Multiply $- 7.5$ by $- 2$ .

$6 x^{2} - 3 x - 3 - 2 \cdot 3 x \cdot x + 15 x = 0$

Step 1.1.6

Simplify each term.

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Step 1.1.6.1

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

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Step 1.1.6.1.1

Move $x$ .

$6 x^{2} - 3 x - 3 - 2 \cdot 3 (x \cdot x) + 15 x = 0$

Step 1.1.6.1.2

Multiply $x$ by $x$ .

$6 x^{2} - 3 x - 3 - 2 \cdot 3 x^{2} + 15 x = 0$

Step 1.1.6.2

Multiply $- 2$ by $3$ .

$6 x^{2} - 3 x - 3 - 6 x^{2} + 15 x = 0$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $6 x^{2} - 3 x - 3 - 6 x^{2} + 15 x$ .

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Step 1.2.1.1

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

$- 3 x - 3 + 0 + 15 x = 0$

Step 1.2.1.2

Add $- 3 x - 3$ and $0$ .

$- 3 x - 3 + 15 x = 0$

Step 1.2.2

Add $- 3 x$ and $15 x$ .

$12 x - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$12 x = 3$

Step 3

Divide each term in $12 x = 3$ by $12$ and simplify.

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Step 3.1

Divide each term in $12 x = 3$ by $12$ .

$\frac{12 x}{12} = \frac{3}{12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{3}{12}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $3$ and $12$ .

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Step 3.3.1.1

Factor $3$ out of $3$ .

$x = \frac{3 (1)}{12}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $3$ out of $12$ .

$x = \frac{3 \cdot 1}{3 \cdot 4}$

Step 3.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 1}{3 \cdot 4}$

Step 3.3.1.2.3

Rewrite the expression.

$x = \frac{1}{4}$

Step 3.3.2

Divide $1$ by $4$ .

$x = 0.25$