Find a,b,c 2x(9-5x)=-5x(2-3x)

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

Step 1

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

Simplify the left side.

Simplify $2 x (9 - 5 x)$ .

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

Multiply $9$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 5$ .

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

Simplify the right side.

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

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

Multiply $2$ by $- 5$ .

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

Rewrite using the commutative property of multiplication.

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

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 5$ by $- 3$ .

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

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

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

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

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

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

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

Add $18 x$ and $10 x$ .

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

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.

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

Find a,b,c 2x(9-5x)=-5x(2-3x)

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