Solve (5-x)(6+2x)=-2+4x Using the Distributive Property

Solve the following equation using the distributive property:

$(5-x)(6+2x)=-2+4x$

To solve the given equation $(5-x)(6+2x)=-2+4x$, we'll apply the following steps to use the distributive property:

• Step 1: Expand the left side using the distributive property:
  $(5-x)(6+2x) = 5 \cdot 6 + 5 \cdot 2x - x \cdot 6 - x \cdot 2x$ $= 30 + 10x - 6x - 2x^2$ Finally, combine like terms:
  $= -2x^2 + 4x + 30$
• Step 2: Set the equation against the right side:
  $-2x^2 + 4x + 30 = -2 + 4x$
• Step 3: Move all terms to one side of the equation:
  $-2x^2 + 4x + 30 - 4x - (-2) = 0$ Simplify to:
  $-2x^2 + 32 = 0$
• Step 4: Solve the quadratic equation:
  Factor out the common term:
  $-2(x^2 - 16) = 0$
  $x^2 - 16 = 0$
• Step 5: Solve for $x$:
  $x^2 = 16$
  $x = \pm 4$

Therefore, the solution to the equation is $x = \pm 4$.