Algebra Examples

$2 x (9 - 5 x) = - 5 x (2 - 3 x)$

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 $2 x (9 - 5 x)$ .

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Step 1.1.1.1

Simplify by multiplying through.

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Step 1.1.1.1.1

Apply the distributive property.

$2 x \cdot 9 + 2 x (- 5 x) = - 5 x (2 - 3 x)$

Step 1.1.1.1.2

Simplify the expression.

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Step 1.1.1.1.2.1

Multiply $9$ by $2$ .

$18 x + 2 x (- 5 x) = - 5 x (2 - 3 x)$

Step 1.1.1.1.2.2

Rewrite using the commutative property of multiplication.

$18 x + 2 \cdot - 5 x \cdot x = - 5 x (2 - 3 x)$

Step 1.1.1.2

Simplify each term.

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Step 1.1.1.2.1

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

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Step 1.1.1.2.1.1

Move $x$ .

$18 x + 2 \cdot - 5 (x \cdot x) = - 5 x (2 - 3 x)$

Step 1.1.1.2.1.2

Multiply $x$ by $x$ .

$18 x + 2 \cdot - 5 x^{2} = - 5 x (2 - 3 x)$

Step 1.1.1.2.2

Multiply $2$ by $- 5$ .

$18 x - 10 x^{2} = - 5 x (2 - 3 x)$

Step 1.2

Simplify the right side.

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Step 1.2.1

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

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Step 1.2.1.1

Simplify by multiplying through.

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Step 1.2.1.1.1

Apply the distributive property.

$18 x - 10 x^{2} = - 5 x \cdot 2 - 5 x (- 3 x)$

Step 1.2.1.1.2

Simplify the expression.

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Step 1.2.1.1.2.1

Multiply $2$ by $- 5$ .

$18 x - 10 x^{2} = - 10 x - 5 x (- 3 x)$

Step 1.2.1.1.2.2

Rewrite using the commutative property of multiplication.

$18 x - 10 x^{2} = - 10 x - 5 \cdot - 3 x \cdot x$

Step 1.2.1.2

Simplify each term.

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Step 1.2.1.2.1

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

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Step 1.2.1.2.1.1

Move $x$ .

$18 x - 10 x^{2} = - 10 x - 5 \cdot - 3 (x \cdot x)$

Step 1.2.1.2.1.2

Multiply $x$ by $x$ .

$18 x - 10 x^{2} = - 10 x - 5 \cdot - 3 x^{2}$

Step 1.2.1.2.2

Multiply $- 5$ by $- 3$ .

$18 x - 10 x^{2} = - 10 x + 15 x^{2}$

Step 1.3

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

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Step 1.3.1

Add $10 x$ to both sides of the equation.

$18 x - 10 x^{2} + 10 x = 15 x^{2}$

Step 1.3.2

Subtract $15 x^{2}$ from both sides of the equation.

$18 x - 10 x^{2} + 10 x - 15 x^{2} = 0$

Step 1.4

Simplify $18 x - 10 x^{2} + 10 x - 15 x^{2}$ .

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Step 1.4.1

Add $18 x$ and $10 x$ .

$- 10 x^{2} + 28 x - 15 x^{2} = 0$

Step 1.4.2

Subtract $15 x^{2}$ from $- 10 x^{2}$ .

$- 25 x^{2} + 28 x = 0$

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.

$a = - 25$ , $b = 28$ , $c = 0$