Solve for a (a-4b)/(-2a+4b)=-8

a-4b-2a+4b=-8
Factor 2 out of -2a+4b.
Factor 2 out of -2a.
a-4b2(-a)+4b=-8
Factor 2 out of 4b.
a-4b2(-a)+2(2b)=-8
Factor 2 out of 2(-a)+2(2b).
a-4b2(-a+2b)=-8
a-4b2(-a+2b)=-8
Solve for a.
Multiply each term by -a+2b and simplify.
Multiply each term in a-4b2(-a+2b)=-8 by -a+2b.
a-4b2(-a+2b)⋅(-a+2b)=-8⋅(-a+2b)
Cancel the common factor of -a+2b.
Factor -a+2b out of 2(-a+2b).
a-4b(-a+2b)⋅2⋅(-a+2b)=-8⋅(-a+2b)
Cancel the common factor.
a-4b(-a+2b)⋅2⋅(-a+2b)=-8⋅(-a+2b)
Rewrite the expression.
a-4b2=-8⋅(-a+2b)
a-4b2=-8⋅(-a+2b)
Simplify -8⋅(-a+2b).
Apply the distributive property.
a-4b2=-8(-a)-8(2b)
Multiply.
Multiply -1 by -8.
a-4b2=8a-8(2b)
Multiply 2 by -8.
a-4b2=8a-16b
a-4b2=8a-16b
a-4b2=8a-16b
a-4b2=8a-16b
Multiply both sides of the equation by 2.
a-4b=8a⋅(2)-16b⋅2
Remove parentheses.
a-4b=8a⋅(2)-16b⋅2
Simplify each term.
Multiply 2 by 8.
a-4b=16a-16b⋅2
Multiply 2 by -16.
a-4b=16a-32b
a-4b=16a-32b
Move all terms containing a to the left side of the equation.
Subtract 16a from both sides of the equation.
a-4b-16a=-32b
Subtract 16a from a.
-15a-4b=-32b
-15a-4b=-32b
Move all terms not containing a to the right side of the equation.
Add 4b to both sides of the equation.
-15a=-32b+4b
-15a=-28b
-15a=-28b
Divide each term by -15 and simplify.
Divide each term in -15a=-28b by -15.
-15a-15=-28b-15
Cancel the common factor of -15.
Cancel the common factor.
-15a-15=-28b-15
Divide a by 1.
a=-28b-15
a=-28b-15
Dividing two negative values results in a positive value.
a=28b15
a=28b15
a=28b15
Solve for a (a-4b)/(-2a+4b)=-8

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