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⋅6+5⋅2x−x⋅6−x⋅2x
=30+10x−6x−2x2
Finally, combine like terms:
=−2x2+4x+30
- Step 2: Set the equation against the right side:
−2x2+4x+30=−2+4x
- Step 3: Move all terms to one side of the equation:
−2x2+4x+30−4x−(−2)=0
Simplify to:
−2x2+32=0
- Step 4: Solve the quadratic equation:
Factor out the common term:
−2(x2−16)=0
x2−16=0
- Step 5: Solve for x:
x2=16
x=±4
Therefore, the solution to the equation is x=±4.