Precalculus Examples

${(3 x - 2)}^{2} = (x - 5) (9 x + 4)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(x - 5) (9 x + 4) = {(3 x - 2)}^{2}$

Step 2

Simplify $(x - 5) (9 x + 4)$ .

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Step 2.1

Rewrite.

$0 + 0 + (x - 5) (9 x + 4) = {(3 x - 2)}^{2}$

Step 2.2

Simplify by adding zeros.

$(x - 5) (9 x + 4) = {(3 x - 2)}^{2}$

Step 2.3

Expand $(x - 5) (9 x + 4)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$x (9 x + 4) - 5 (9 x + 4) = {(3 x - 2)}^{2}$

Step 2.3.2

Apply the distributive property.

$x (9 x) + x \cdot 4 - 5 (9 x + 4) = {(3 x - 2)}^{2}$

Step 2.3.3

Apply the distributive property.

$x (9 x) + x \cdot 4 - 5 (9 x) - 5 \cdot 4 = {(3 x - 2)}^{2}$

Step 2.4

Simplify and combine like terms.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Rewrite using the commutative property of multiplication.

$9 x \cdot x + x \cdot 4 - 5 (9 x) - 5 \cdot 4 = {(3 x - 2)}^{2}$

Step 2.4.1.2

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

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Step 2.4.1.2.1

Move $x$ .

$9 (x \cdot x) + x \cdot 4 - 5 (9 x) - 5 \cdot 4 = {(3 x - 2)}^{2}$

Step 2.4.1.2.2

Multiply $x$ by $x$ .

$9 x^{2} + x \cdot 4 - 5 (9 x) - 5 \cdot 4 = {(3 x - 2)}^{2}$

Step 2.4.1.3

Move $4$ to the left of $x$ .

$9 x^{2} + 4 \cdot x - 5 (9 x) - 5 \cdot 4 = {(3 x - 2)}^{2}$

Step 2.4.1.4

Multiply $9$ by $- 5$ .

$9 x^{2} + 4 x - 45 x - 5 \cdot 4 = {(3 x - 2)}^{2}$

Step 2.4.1.5

Multiply $- 5$ by $4$ .

$9 x^{2} + 4 x - 45 x - 20 = {(3 x - 2)}^{2}$

Step 2.4.2

Subtract $45 x$ from $4 x$ .

$9 x^{2} - 41 x - 20 = {(3 x - 2)}^{2}$

Step 3

Simplify ${(3 x - 2)}^{2}$ .

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Step 3.1

Rewrite ${(3 x - 2)}^{2}$ as $(3 x - 2) (3 x - 2)$ .

$9 x^{2} - 41 x - 20 = (3 x - 2) (3 x - 2)$

Step 3.2

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

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Step 3.2.1

Apply the distributive property.

$9 x^{2} - 41 x - 20 = 3 x (3 x - 2) - 2 (3 x - 2)$

Step 3.2.2

Apply the distributive property.

$9 x^{2} - 41 x - 20 = 3 x (3 x) + 3 x \cdot - 2 - 2 (3 x - 2)$

Step 3.2.3

Apply the distributive property.

$9 x^{2} - 41 x - 20 = 3 x (3 x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Step 3.3

Simplify and combine like terms.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Rewrite using the commutative property of multiplication.

$9 x^{2} - 41 x - 20 = 3 \cdot 3 x \cdot x + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Step 3.3.1.2

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

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Step 3.3.1.2.1

Move $x$ .

$9 x^{2} - 41 x - 20 = 3 \cdot 3 (x \cdot x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Step 3.3.1.2.2

Multiply $x$ by $x$ .

$9 x^{2} - 41 x - 20 = 3 \cdot 3 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Step 3.3.1.3

Multiply $3$ by $3$ .

$9 x^{2} - 41 x - 20 = 9 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Step 3.3.1.4

Multiply $- 2$ by $3$ .

$9 x^{2} - 41 x - 20 = 9 x^{2} - 6 x - 2 (3 x) - 2 \cdot - 2$

Step 3.3.1.5

Multiply $3$ by $- 2$ .

$9 x^{2} - 41 x - 20 = 9 x^{2} - 6 x - 6 x - 2 \cdot - 2$

Step 3.3.1.6

Multiply $- 2$ by $- 2$ .

$9 x^{2} - 41 x - 20 = 9 x^{2} - 6 x - 6 x + 4$

Step 3.3.2

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

$9 x^{2} - 41 x - 20 = 9 x^{2} - 12 x + 4$

Step 4

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

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Step 4.1

Subtract $9 x^{2}$ from both sides of the equation.

$9 x^{2} - 41 x - 20 - 9 x^{2} = - 12 x + 4$

Step 4.2

Add $12 x$ to both sides of the equation.

$9 x^{2} - 41 x - 20 - 9 x^{2} + 12 x = 4$

Step 4.3

Combine the opposite terms in $9 x^{2} - 41 x - 20 - 9 x^{2} + 12 x$ .

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Step 4.3.1

Subtract $9 x^{2}$ from $9 x^{2}$ .

$- 41 x - 20 + 0 + 12 x = 4$

Step 4.3.2

Add $- 41 x - 20$ and $0$ .

$- 41 x - 20 + 12 x = 4$

Step 4.4

Add $- 41 x$ and $12 x$ .

$- 29 x - 20 = 4$

Step 5

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

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Step 5.1

Add $20$ to both sides of the equation.

$- 29 x = 4 + 20$

Step 5.2

Add $4$ and $20$ .

$- 29 x = 24$

Step 6

Divide each term in $- 29 x = 24$ by $- 29$ and simplify.

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Step 6.1

Divide each term in $- 29 x = 24$ by $- 29$ .

$\frac{- 29 x}{- 29} = \frac{24}{- 29}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 29$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 29 x}{- 29} = \frac{24}{- 29}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{- 29}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$x = - \frac{24}{29}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{24}{29}$

Decimal Form:

$x = - 0.82758620 \dots$