Solve for x (2x-1)(3x+2)=x+292

$(2 x - 1) (3 x + 2) = x + 292$

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

Rewrite.

$0 + 0 + (2 x - 1) (3 x + 2) = x + 292$

Simplify by adding zeros.

$(2 x - 1) (3 x + 2) = x + 292$

Expand $(2 x - 1) (3 x + 2)$ using the FOIL Method.

Apply the distributive property.

$2 x (3 x + 2) - 1 (3 x + 2) = x + 292$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot 2 - 1 (3 x + 2) = x + 292$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot 2 - 1 (3 x) - 1 \cdot 2 = x + 292$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x \cdot 2 - 1 (3 x) - 1 \cdot 2 = x + 292$

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

Move $x$ .

$2 \cdot 3 (x \cdot x) + 2 x \cdot 2 - 1 (3 x) - 1 \cdot 2 = x + 292$

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} + 2 x \cdot 2 - 1 (3 x) - 1 \cdot 2 = x + 292$

Multiply $2$ by $3$ .

$6 x^{2} + 2 x \cdot 2 - 1 (3 x) - 1 \cdot 2 = x + 292$

Multiply $2$ by $2$ .

$6 x^{2} + 4 x - 1 (3 x) - 1 \cdot 2 = x + 292$

Multiply $3$ by $- 1$ .

$6 x^{2} + 4 x - 3 x - 1 \cdot 2 = x + 292$

Multiply $- 1$ by $2$ .

$6 x^{2} + 4 x - 3 x - 2 = x + 292$

Subtract $3 x$ from $4 x$ .

$6 x^{2} + x - 2 = x + 292$

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

Subtract $x$ from both sides of the equation.

$6 x^{2} + x - 2 - x = 292$

Combine the opposite terms in $6 x^{2} + x - 2 - x$ .

Subtract $x$ from $x$ .

$6 x^{2} + 0 - 2 = 292$

Add $6 x^{2}$ and $0$ .

$6 x^{2} - 2 = 292$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$6 x^{2} = 292 + 2$

Add $292$ and $2$ .

$6 x^{2} = 294$

Divide each term in $6 x^{2} = 294$ by $6$ and simplify.

Divide each term in $6 x^{2} = 294$ by $6$ .

$\frac{6 x^{2}}{6} = \frac{294}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x^{2}}{6} = \frac{294}{6}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{294}{6}$

Simplify the right side.

Divide $294$ by $6$ .

$x^{2} = 49$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 7$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 7$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 7$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 7, - 7$

Solve for x (2x-1)(3x+2)=x+292

Related Questions

Support LCMGCF.com by disabling your adblocker.