4x2+7=7+24x

To solve the equation \(4x^2 + 7 = 7 + 24x\), we first simplify it.

1. Subtract \(7\) from both sides:

\[ 4x^2 + 7 - 7 = 7 + 24x - 7 \] \[ 4x^2 = 24x \]

2. Rearranging gives us:

\[ 4x^2 - 24x = 0 \]

3. Factor out a common term (\(4x\)):

\[ 4x(x - 6) = 0 \]

4. Set each factor to zero:

\[ 4x = 0 \quad \Rightarrow \quad x = 0 \] \[ x - 6 = 0 \quad \Rightarrow \quad x = 6 \]

Thus, the solutions to the equation are:

\[ x = 0 \quad \text{and} \quad x = 6 \]