To solve the equation [tex]\(12b^2 - 15b = -11b\)[/tex], we can follow these steps:
1. Combine like terms on one side of the equation:
[tex]\[
12b^2 - 15b + 11b = 0
\][/tex]
2. Simplify the equation:
[tex]\[
12b^2 - 4b = 0
\][/tex]
3. Factor out the common term, [tex]\(b\)[/tex]:
[tex]\[
b(12b - 4) = 0
\][/tex]
4. Set each factor equal to zero and solve for [tex]\(b\)[/tex]:
The first factor is [tex]\(b = 0\)[/tex].
[tex]\[
b = 0
\][/tex]
The second factor is:
[tex]\[
12b - 4 = 0
\][/tex]
Solving for [tex]\(b\)[/tex]:
[tex]\[
12b = 4
\][/tex]
[tex]\[
b = \frac{4}{12}
\][/tex]
[tex]\[
b = \frac{1}{3}
\][/tex]
Therefore, the solutions to the equation are:
[tex]\[
b = 0, \frac{1}{3}
\][/tex]
