The first step to solving this equation is to simplify the left-hand side by using the distributive property:
x(2x+4) = 6x+24
2x^2 + 4x = 6x + 24
Next, we can move all the terms to one side of the equation and simplify:
2x^2 - 2x - 24 = 0
Factor out the common factor of 2:
2(x^2 - x - 12) = 0
Factor the \quadratic expression in parentheses using the product-sum method:
2(x-4)(x+3) = 0
Using the zero product property, we can set each factor equal to zero:
x-4=0 or x+3=0
Solving for x, we get:
x = 4 or x = -3
Therefore, the solutions to x(2x+4) = 6x+24 are x = 4 and x = -3.
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