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Question
x\left(x-c\right)=1-c
Solve the equation
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\text{Solve for }x
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\text{Solve for }c
\begin{align}&x=c-1\\&x=1\end{align}
Evaluate
x\left(x-c\right)=1-c
Expand the expression
More Steps
Evaluate
x\left(x-c\right)
Apply the distributive property
x\times x-xc
Multiply the terms
x^{2}-xc
Multiply the terms
x^{2}-cx
x^{2}-cx=1-c
Move the expression to the left side
x^{2}-cx-\left(1-c\right)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x^{2}-cx-1+c=0
Factor the expression
More Steps
Evaluate
x^{2}-cx-1+c
Calculate
x^{2}-x-cx+c+x-1
Rewrite the expression
x\times x-x-cx+c+x-1
\text{Factor out }x\text{ from the expression}
x\left(x-1\right)-cx+c+x-1
\text{Factor out }-c\text{ from the expression}
x\left(x-1\right)-c\left(x-1\right)+x-1
\text{Factor out }x-1\text{ from the expression}
\left(x-c+1\right)\left(x-1\right)
\left(x-c+1\right)\left(x-1\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-c+1=0\\&x-1=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x-c+1=0
Move the expression to the right-hand side and change its sign
x=0-\left(-c+1\right)
Subtract the terms
More Steps
Evaluate
0-\left(-c+1\right)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
0+c-1
Removing 0 doesn't change the value,so remove it from the expression
c-1
x=c-1
\begin{align}&x=c-1\\&x-1=0\end{align}
Solution
More Steps
Evaluate
x-1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
\begin{align}&x=c-1\\&x=1\end{align}
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