Write as a Set of Linear Factors 3x^2+35=7x^2-4x

$3 x^{2} + 35 = 7 x^{2} - 4 x$

Step 1

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

Subtract $7 x^{2}$ from both sides of the equation.

$3 x^{2} + 35 - 7 x^{2} = - 4 x$

Add $4 x$ to both sides of the equation.

$3 x^{2} + 35 - 7 x^{2} + 4 x = 0$

Step 2

Subtract $7 x^{2}$ from $3 x^{2}$ .

$- 4 x^{2} + 35 + 4 x = 0$

Step 3

Factor $- 1$ out of $- 4 x^{2} + 35 + 4 x$ .

Move $35$ .

$- 4 x^{2} + 4 x + 35 = 0$

Factor $- 1$ out of $- 4 x^{2}$ .

$- (4 x^{2}) + 4 x + 35 = 0$

Factor $- 1$ out of $4 x$ .

$- (4 x^{2}) - (- 4 x) + 35 = 0$

Rewrite $35$ as $- 1 (- 35)$ .

$- (4 x^{2}) - (- 4 x) - 1 \cdot - 35 = 0$

Factor $- 1$ out of $- (4 x^{2}) - (- 4 x)$ .

$- (4 x^{2} - 4 x) - 1 \cdot - 35 = 0$

Factor $- 1$ out of $- (4 x^{2} - 4 x) - 1 (- 35)$ .

$- (4 x^{2} - 4 x - 35) = 0$

Step 4

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 35 = - 140$ and whose sum is $b = - 4$ .

Factor $- 4$ out of $- 4 x$ .

$- (4 x^{2} - 4 x - 35) = 0$

Rewrite $- 4$ as $10$ plus $- 14$

$- (4 x^{2} + (10 - 14) x - 35) = 0$

Apply the distributive property.

$- (4 x^{2} + 10 x - 14 x - 35) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((4 x^{2} + 10 x) - 14 x - 35) = 0$

Factor out the greatest common factor (GCF) from each group.

$- (2 x (2 x + 5) - 7 (2 x + 5)) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x + 5$ .

$- ((2 x + 5) (2 x - 7)) = 0$

Remove unnecessary parentheses.

$- (2 x + 5) (2 x - 7) = 0$

Write as a Set of Linear Factors 3x^2+35=7x^2-4x

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