6а²-(а+2)²=-4(а-4)

To solve the equation \( 6a^2 - (a + 2)^2 = -4(a - 4) \), let's start by simplifying both sides step by step. ### Step 1: Expand the squared term and the right side: 1. Expand \((a + 2)^2\): \[ (a + 2)^2 = a^2 + 4a + 4 \] 2. Expand \(-4(a - 4)\): \[ -4(a - 4) = -4a + 16 \] ### Step 2: Substitute these expansions into the equation: The equation now looks like this: \[ 6a^2 - (a^2 + 4a + 4) = -4a + 16 \] ### Step 3: Simplify the left side: Combine the terms on the left: \[ 6a^2 - a^2 - 4a - 4 = -4a + 16 \] \[ 5a^2 - 4a - 4 = -4a + 16 \] ### Step 4: Move all terms to one side of the equation: Add \(4a\) to both sides: \[ 5a^2 - 4 = 16 \] Next, subtract \(16\) from both sides: \[ 5a^2 - 4 - 16 = 0 \] \[ 5a^2 - 20 = 0 \] ### Step 5: Simplify further: Add \(20\) to both sides: \[ 5a^2 = 20 \] Divide by \(5\): \[ a^2 = 4 \] ### Step 6: Solve for \(a\): Take the square root of both sides: \[ a = 2 \quad \text{or} \quad a = -2 \] ### Final Answer: Thus, the solutions to the equation \( 6a^2 - (a + 2)^2 = -4(a - 4) \) are: \[ a = 2 \quad \text{and} \quad a = -2 \]