Solve for b. 10b^2-15b= 8b -12

Set Equation Equal: First, we need to bring all terms to one side of the equation to set it equal to zero. 10b^2 - 15b - (8b - 12) = 0Distribute Negative Sign: Now, distribute the negative sign to the terms inside the parentheses. 10b^2 - 15b - 8b + 12 = 0Combine Like Terms: Combine like terms. 10b^2 - 23b + 12 = 0Find Factoring Numbers: Next, we need to factor the quadratic equation. We are looking for two numbers that multiply to 10*12 (120) and add up to -23.Write Factored Form: The numbers that satisfy these conditions are -20 and -3 because -20 * -3 = 120 and -20 + -3 = -23.Factor by Grouping: Now we can write the factored form using these two numbers. (10b^2 - 20b) + (-3b + 12) = 0Final Factored Form: Factor by grouping. Take out the common factor of 10b from the first group and -3 from the second group. 10b(b - 2) - 3(b - 2) = 0Since both groups contain the common factor (b - 2), we can factor it out. (b - 2)(10b - 3) = 0

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Solve for $b$ . $\newline$ $10b^2-15b= 8b -12$

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\newline

10b^2-15b= 8b -12

Set Equation Equal: First, we need to bring all terms to one side of the equation to set it equal to zero. $\newline$ $10b^2 - 15b - (8b - 12) = 0$
Distribute Negative Sign: Now, distribute the negative sign to the terms inside the parentheses. $10b^2 - 15b - 8b + 12 = 0$
Combine Like Terms: Combine like terms. $\newline$ $10b^2 - 23b + 12 = 0$
Find Factoring Numbers: Next, we need to factor the quadratic equation. We are looking for two numbers that multiply to $10\times12$ ( $120$ ) and add up to $-23$ .
Write Factored Form: The numbers that satisfy these conditions are $-20$ and $-3$ because $-20 \times -3 = 120$ and $-20 + -3 = -23$ .
Factor by Grouping: Now we can write the factored form using these two numbers. $10b^2 - 20b$ + $-3b + 12$ = $0$
Final Factored Form: Factor by grouping. Take out the common factor of $10b$ from the first group and $-3$ from the second group. $\newline$ $10b(b - 2) - 3(b - 2) = 0$
Final Factored Form: Factor by grouping. Take out the common factor of $10b$ from the first group and $-3$ from the second group. $\newline$ $10b(b - 2) - 3(b - 2) = 0$ Since both groups contain the common factor $(b - 2)$ , we can factor it out. $\newline$ $(b - 2)(10b - 3) = 0$