32) 2x - 4x^2 + 6 = 3x - (2x^2 - 3) - 2x^2

Solution:

• Simplify the right side of the equation: \( 3x - 2x^2 + 3 - 2x^2 = 3x - 4x^2 + 3 \)
• Set up the equation: \( -4x^2 + 2x + 6 = -4x^2 + 3x + 3 \)
• Add \( 4x^2 \) to both sides: \( 2x + 6 = 3x + 3 \)
• Subtract \( 2x \) from both sides: \( 6 = x + 3 \)
• Subtract 3 from both sides: \( 3 = x \)

Final Answer: x = 3