Write in Standard Form 13-6x=(2x-5)^2+3

$13 - 6 x = {(2 x - 5)}^{2} + 3$

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

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

$13 - 6 x - {(2 x - 5)}^{2} = 3$

Subtract $3$ from both sides of the equation.

$13 - 6 x - {(2 x - 5)}^{2} - 3 = 0$

Simplify $13 - 6 x - {(2 x - 5)}^{2} - 3$ .

Simplify each term.

Rewrite ${(2 x - 5)}^{2}$ as $(2 x - 5) (2 x - 5)$ .

$13 - 6 x - ((2 x - 5) (2 x - 5)) - 3 = 0$

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

Apply the distributive property.

$13 - 6 x - (2 x (2 x - 5) - 5 (2 x - 5)) - 3 = 0$

Apply the distributive property.

$13 - 6 x - (2 x (2 x) + 2 x \cdot - 5 - 5 (2 x - 5)) - 3 = 0$

Apply the distributive property.

$13 - 6 x - (2 x (2 x) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 3 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$13 - 6 x - (2 \cdot 2 x \cdot x + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 3 = 0$

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

Move $x$ .

$13 - 6 x - (2 \cdot 2 (x \cdot x) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 3 = 0$

Multiply $x$ by $x$ .

$13 - 6 x - (2 \cdot 2 x^{2} + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 3 = 0$

Multiply $2$ by $2$ .

$13 - 6 x - (4 x^{2} + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5) - 3 = 0$

Multiply $- 5$ by $2$ .

$13 - 6 x - (4 x^{2} - 10 x - 5 (2 x) - 5 \cdot - 5) - 3 = 0$

Multiply $2$ by $- 5$ .

$13 - 6 x - (4 x^{2} - 10 x - 10 x - 5 \cdot - 5) - 3 = 0$

Multiply $- 5$ by $- 5$ .

$13 - 6 x - (4 x^{2} - 10 x - 10 x + 25) - 3 = 0$

Subtract $10 x$ from $- 10 x$ .

$13 - 6 x - (4 x^{2} - 20 x + 25) - 3 = 0$

Apply the distributive property.

$13 - 6 x - (4 x^{2}) - (- 20 x) - 1 \cdot 25 - 3 = 0$

Simplify.

Multiply $4$ by $- 1$ .

$13 - 6 x - 4 x^{2} - (- 20 x) - 1 \cdot 25 - 3 = 0$

Multiply $- 20$ by $- 1$ .

$13 - 6 x - 4 x^{2} + 20 x - 1 \cdot 25 - 3 = 0$

Multiply $- 1$ by $25$ .

$13 - 6 x - 4 x^{2} + 20 x - 25 - 3 = 0$

Subtract $25$ from $13$ .

$- 6 x - 4 x^{2} + 20 x - 12 - 3 = 0$

Add $- 6 x$ and $20 x$ .

$- 4 x^{2} + 14 x - 12 - 3 = 0$

Subtract $3$ from $- 12$ .

$- 4 x^{2} + 14 x - 15 = 0$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

The standard form is $- 4 x^{2} + 14 x - 15$ .

$- 4 x^{2} + 14 x - 15 = 0$

Write in Standard Form 13-6x=(2x-5)^2+3

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