Solve the Equation: (x+2)(2x-4) = 2x²+x+10

To solve this problem, we'll follow these steps:

• Step 1: Expand the left-hand side of the equation.
• Step 2: Set the equation to standard quadratic form.
• Step 3: Factor the quadratic equation.
• Step 4: Solve for $x$.

Let's proceed through each step:

Step 1: Expand the left-hand side using the distributive property:

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

$= 2x^2 - 4x + 4x - 8$

$= 2x^2 - 8$

Step 2: Set the equation to quadratic form:

Set the expanded result equal to the right-hand side:

$2x^2 - 8 = 2x^2 + x + 10$

Step 3: Subtract the right-hand side from the left:

$2x^2 - 8 - (2x^2 + x + 10) = 0$

Simplify:

$2x^2 - 8 - 2x^2 - x - 10 = 0$

$-x - 18 = 0$

Step 4: Solve for $x$:

$-x = 18$

Divide by -1:

$x = -18$

Therefore, the solution to the problem is $x = -18$.

Checking against the given choices, choice 1 matches: $-18$.