Rearrange this equation to isolate c.
a=b((1/c)-(1-d))
a = b (-d-c)/cd
Multiply cd times both sides then distribute the b.
acd = -bd-bc
add bc to both sides:
acd+bc = -bd
factor out the c
c(ad+b) = -bd
Divide both sides by (ad+b) to solve for c.
To isolate variable c in the equation a = b((1/c) - (1-d)), we can follow these steps:
Step 1: Distribute the b through the two terms inside the parentheses:
a = b(1/c) - b(1-d)
Step 2: Simplify the expression by finding a common denominator for the fractions:
a = b/d - b(1-d)
Step 3: Multiply both terms in the second term by c to eliminate the denominator:
a = b/d - bc(1-d)
Step 4: Distribute the b and -bc across the expression:
a = b/d - bc + bcd(1-d)
Step 5: Combine like terms:
a = b/d - bc + bcd - bcd^2
Step 6: Rearrange the terms involving c on one side and constants on the other side:
a + bc = b/d + bcd - bcd^2
Step 7: Factor out c from the terms with c:
a + bc = b/d + bcd(1 - d)
Step 8: Divide the entire equation by (1-d) to isolate c:
(a + bc)/(1-d) = (b/d + bcd(1 - d))/(1-d)
So, after following these steps, the equation is rearranged to isolate c as:
c = (a + bc)/(b/d + bcd(1 - d))/(1-d)
To isolate c in the equation a = b((1/c) - (1-d)), we can follow these steps:
Step 1: Distribute b to the terms inside the parentheses:
a = b/c - b(1-d)
Step 2: Bring the term - b(1-d) to the right side of the equation by subtracting it from both sides:
a + b(1-d) = b/c
Step 3: Multiply both sides of the equation by c to eliminate the fraction:
c(a + b(1-d)) = b
Step 4: Distribute c to the terms on the left side of the equation:
ac + bc(1-d) = b
Step 5: Move the term containing c to the right side by subtracting it from both sides:
bc(1-d) = b - ac
Step 6: Divide both sides of the equation by (1-d) to solve for c:
c = (b - ac)/(bc(1-d))