Solve for x 3x^2+x-1=(2x+9)(x-1)

$3 x^{2} + x - 1 = (2 x + 9) (x - 1)$

Simplify $(2 x + 9) (x - 1)$ .

Rewrite.

$3 x^{2} + x - 1 = 0 + 0 + (2 x + 9) (x - 1)$

Simplify by adding zeros.

$3 x^{2} + x - 1 = (2 x + 9) (x - 1)$

Expand $(2 x + 9) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$3 x^{2} + x - 1 = 2 x (x - 1) + 9 (x - 1)$

Apply the distributive property.

$3 x^{2} + x - 1 = 2 x \cdot x + 2 x \cdot - 1 + 9 (x - 1)$

Apply the distributive property.

$3 x^{2} + x - 1 = 2 x \cdot x + 2 x \cdot - 1 + 9 x + 9 \cdot - 1$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$3 x^{2} + x - 1 = 2 (x \cdot x) + 2 x \cdot - 1 + 9 x + 9 \cdot - 1$

Multiply $x$ by $x$ .

$3 x^{2} + x - 1 = 2 x^{2} + 2 x \cdot - 1 + 9 x + 9 \cdot - 1$

Multiply $- 1$ by $2$ .

$3 x^{2} + x - 1 = 2 x^{2} - 2 x + 9 x + 9 \cdot - 1$

Multiply $9$ by $- 1$ .

$3 x^{2} + x - 1 = 2 x^{2} - 2 x + 9 x - 9$

Add $- 2 x$ and $9 x$ .

$3 x^{2} + x - 1 = 2 x^{2} + 7 x - 9$

Move all terms containing $x$ to the left side of the equation.

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

$3 x^{2} + x - 1 - 2 x^{2} = 7 x - 9$

Subtract $7 x$ from both sides of the equation.

$3 x^{2} + x - 1 - 2 x^{2} - 7 x = - 9$

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

$x^{2} + x - 1 - 7 x = - 9$

Subtract $7 x$ from $x$ .

$x^{2} - 6 x - 1 = - 9$

Add $9$ to both sides of the equation.

$x^{2} - 6 x - 1 + 9 = 0$

Add $- 1$ and $9$ .

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

Factor $x^{2} - 6 x + 8$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $8$ and whose sum is $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$(x - 4) (x - 2) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 4 = 0$

$x - 2 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $(x - 4) (x - 2) = 0$ true.

$x = 4, 2$

Solve for x 3x^2+x-1=(2x+9)(x-1)

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