Algebra Examples

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

Step 1

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

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Step 1.1

Simplify the right side.

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Step 1.1.1

Simplify $4 (3 x - 5)$ .

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Step 1.1.1.1

Apply the distributive property.

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

Step 1.1.1.2

Multiply.

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Step 1.1.1.2.1

Multiply $3$ by $4$ .

$2 x^{2} + x + 3 = 12 x + 4 \cdot - 5$

Step 1.1.1.2.2

Multiply $4$ by $- 5$ .

$2 x^{2} + x + 3 = 12 x - 20$

Step 1.2

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

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Step 1.2.1

Subtract $12 x$ from both sides of the equation.

$2 x^{2} + x + 3 - 12 x = - 20$

Step 1.2.2

Add $20$ to both sides of the equation.

$2 x^{2} + x + 3 - 12 x + 20 = 0$

Step 1.3

Simplify $2 x^{2} + x + 3 - 12 x + 20$ .

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Step 1.3.1

Subtract $12 x$ from $x$ .

$2 x^{2} - 11 x + 3 + 20 = 0$

Step 1.3.2

Add $3$ and $20$ .

$2 x^{2} - 11 x + 23 = 0$

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.

$a = 2$ , $b = - 11$ , $c = 23$