Algebra Examples

$(x + 5) (2 x - 3) = 2 (x + 1)$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $(x + 5) (2 x - 3)$ .

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Step 1.1.1.1

Expand $(x + 5) (2 x - 3)$ using the FOIL Method.

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Step 1.1.1.1.1

Apply the distributive property.

$x (2 x - 3) + 5 (2 x - 3) = 2 (x + 1)$

Step 1.1.1.1.2

Apply the distributive property.

$x (2 x) + x \cdot - 3 + 5 (2 x - 3) = 2 (x + 1)$

Step 1.1.1.1.3

Apply the distributive property.

$x (2 x) + x \cdot - 3 + 5 (2 x) + 5 \cdot - 3 = 2 (x + 1)$

Step 1.1.1.2

Simplify and combine like terms.

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Step 1.1.1.2.1

Simplify each term.

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Step 1.1.1.2.1.1

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot - 3 + 5 (2 x) + 5 \cdot - 3 = 2 (x + 1)$

Step 1.1.1.2.1.2

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

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Step 1.1.1.2.1.2.1

Move $x$ .

$2 (x \cdot x) + x \cdot - 3 + 5 (2 x) + 5 \cdot - 3 = 2 (x + 1)$

Step 1.1.1.2.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + x \cdot - 3 + 5 (2 x) + 5 \cdot - 3 = 2 (x + 1)$

Step 1.1.1.2.1.3

Move $- 3$ to the left of $x$ .

$2 x^{2} - 3 \cdot x + 5 (2 x) + 5 \cdot - 3 = 2 (x + 1)$

Step 1.1.1.2.1.4

Multiply $2$ by $5$ .

$2 x^{2} - 3 x + 10 x + 5 \cdot - 3 = 2 (x + 1)$

Step 1.1.1.2.1.5

Multiply $5$ by $- 3$ .

$2 x^{2} - 3 x + 10 x - 15 = 2 (x + 1)$

Step 1.1.1.2.2

Add $- 3 x$ and $10 x$ .

$2 x^{2} + 7 x - 15 = 2 (x + 1)$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $2 (x + 1)$ .

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Step 1.2.1.1

Apply the distributive property.

$2 x^{2} + 7 x - 15 = 2 x + 2 \cdot 1$

Step 1.2.1.2

Multiply $2$ by $1$ .

$2 x^{2} + 7 x - 15 = 2 x + 2$

Step 1.3

Move all the expressions to the left side of the equation.

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Step 1.3.1

Subtract $2 x$ from both sides of the equation.

$2 x^{2} + 7 x - 15 - 2 x = 2$

Step 1.3.2

Subtract $2$ from both sides of the equation.

$2 x^{2} + 7 x - 15 - 2 x - 2 = 0$

Step 1.4

Simplify $2 x^{2} + 7 x - 15 - 2 x - 2$ .

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Step 1.4.1

Subtract $2 x$ from $7 x$ .

$2 x^{2} + 5 x - 15 - 2 = 0$

Step 1.4.2

Subtract $2$ from $- 15$ .

$2 x^{2} + 5 x - 17 = 0$

Step 2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Step 3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 2$ , $b = 5$ , $c = - 17$