To solve the equation \( 4p + 25 = 6(p - 3) - 3(4 - 3p) \), we will first simplify both sides step by step.
Starting with the right side of the equation:
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Distribute the \( 6 \) in \( 6(p - 3) \): \[ 6(p - 3) = 6p - 18 \]
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Distribute the \( -3 \) in \( -3(4 - 3p) \): \[ -3(4 - 3p) = -12 + 9p \]
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Combine the two results: \[ 6(p - 3) - 3(4 - 3p) = 6p - 18 - 12 + 9p = 6p + 9p - 18 - 12 = 15p - 30 \]
Now we can rewrite our equation: \[ 4p + 25 = 15p - 30 \]
Next, we will rearrange this equation to isolate \( p \):
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Subtract \( 4p \) from both sides: \[ 25 = 15p - 4p - 30 \] \[ 25 = 11p - 30 \]
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Add \( 30 \) to both sides: \[ 25 + 30 = 11p \] \[ 55 = 11p \]
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Divide by \( 11 \): \[ p = \frac{55}{11} = 5 \]
Thus, the solution to the equation is: \[ \boxed{5} \]