Algebra Examples

$5 x^{2} + 43 = (x - 1) (5 x + 6)$

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.

$(x - 1) (5 x + 6) = 5 x^{2} + 43$

Step 2

Simplify $(x - 1) (5 x + 6)$ .

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Step 2.1

Rewrite.

$0 + 0 + (x - 1) (5 x + 6) = 5 x^{2} + 43$

Step 2.2

Simplify by adding zeros.

$(x - 1) (5 x + 6) = 5 x^{2} + 43$

Step 2.3

Expand $(x - 1) (5 x + 6)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$x (5 x + 6) - 1 (5 x + 6) = 5 x^{2} + 43$

Step 2.3.2

Apply the distributive property.

$x (5 x) + x \cdot 6 - 1 (5 x + 6) = 5 x^{2} + 43$

Step 2.3.3

Apply the distributive property.

$x (5 x) + x \cdot 6 - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

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.

$5 x \cdot x + x \cdot 6 - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Step 2.4.1.2

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

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Step 2.4.1.2.1

Move $x$ .

$5 (x \cdot x) + x \cdot 6 - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Step 2.4.1.2.2

Multiply $x$ by $x$ .

$5 x^{2} + x \cdot 6 - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Step 2.4.1.3

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

$5 x^{2} + 6 \cdot x - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Step 2.4.1.4

Multiply $5$ by $- 1$ .

$5 x^{2} + 6 x - 5 x - 1 \cdot 6 = 5 x^{2} + 43$

Step 2.4.1.5

Multiply $- 1$ by $6$ .

$5 x^{2} + 6 x - 5 x - 6 = 5 x^{2} + 43$

Step 2.4.2

Subtract $5 x$ from $6 x$ .

$5 x^{2} + x - 6 = 5 x^{2} + 43$

Step 3

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

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Step 3.1

Subtract $5 x^{2}$ from both sides of the equation.

$5 x^{2} + x - 6 - 5 x^{2} = 43$

Step 3.2

Combine the opposite terms in $5 x^{2} + x - 6 - 5 x^{2}$ .

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Step 3.2.1

Subtract $5 x^{2}$ from $5 x^{2}$ .

$x - 6 + 0 = 43$

Step 3.2.2

Add $x - 6$ and $0$ .

$x - 6 = 43$

Step 4

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

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Step 4.1

Add $6$ to both sides of the equation.

$x = 43 + 6$

Step 4.2

Add $43$ and $6$ .

$x = 49$