Algebra Examples

$5 x - 3 x (2 x - 1) + 3 x = 8 + x$

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

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Step 1.1.1.1

Simplify each term.

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Step 1.1.1.1.1

Apply the distributive property.

$5 x - 3 x (2 x) - 3 x \cdot - 1 + 3 x = 8 + x$

Step 1.1.1.1.2

Rewrite using the commutative property of multiplication.

$5 x - 3 \cdot 2 x \cdot x - 3 x \cdot - 1 + 3 x = 8 + x$

Step 1.1.1.1.3

Multiply $- 1$ by $- 3$ .

$5 x - 3 \cdot 2 x \cdot x + 3 x + 3 x = 8 + x$

Step 1.1.1.1.4

Simplify each term.

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Step 1.1.1.1.4.1

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

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Step 1.1.1.1.4.1.1

Move $x$ .

$5 x - 3 \cdot 2 (x \cdot x) + 3 x + 3 x = 8 + x$

Step 1.1.1.1.4.1.2

Multiply $x$ by $x$ .

$5 x - 3 \cdot 2 x^{2} + 3 x + 3 x = 8 + x$

Step 1.1.1.1.4.2

Multiply $- 3$ by $2$ .

$5 x - 6 x^{2} + 3 x + 3 x = 8 + x$

Step 1.1.1.2

Simplify by adding terms.

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Step 1.1.1.2.1

Add $5 x$ and $3 x$ .

$- 6 x^{2} + 8 x + 3 x = 8 + x$

Step 1.1.1.2.2

Add $8 x$ and $3 x$ .

$- 6 x^{2} + 11 x = 8 + x$

Step 1.2

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

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Step 1.2.1

Subtract $8$ from both sides of the equation.

$- 6 x^{2} + 11 x - 8 = x$

Step 1.2.2

Subtract $x$ from both sides of the equation.

$- 6 x^{2} + 11 x - 8 - x = 0$

Step 1.3

Subtract $x$ from $11 x$ .

$- 6 x^{2} + 10 x - 8 = 0$

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.

$a = - 6$ , $b = 10$ , $c = - 8$