To solve the expression [tex]\((20x^2 - 12x) + (25x - 15)\)[/tex], we will factor it step by step.
1. Group the terms:
[tex]\[
(20x^2 - 12x) + (25x - 15)
\][/tex]
2. Factor out the greatest common factor (GCF) from each group:
- For the first group: [tex]\(20x^2 - 12x\)[/tex], the GCF is [tex]\(4x\)[/tex].
[tex]\[
20x^2 - 12x = 4x(5x - 3)
\][/tex]
- For the second group: [tex]\(25x - 15\)[/tex], the GCF is [tex]\(5\)[/tex].
[tex]\[
25x - 15 = 5(5x - 3)
\][/tex]
3. Rewrite the expression with the factored terms:
[tex]\[
(20x^2 - 12x) + (25x - 15) = 4x(5x - 3) + 5(5x - 3)
\][/tex]
4. Notice that both terms have a common factor of [tex]\((5x - 3)\)[/tex]:
- Factor out the common factor [tex]\((5x - 3)\)[/tex] from both terms.
[tex]\[
4x(5x - 3) + 5(5x - 3) = (5x - 3)(4x + 5)
\][/tex]
So, the fully factored form of the expression [tex]\((20x^2 - 12x) + (25x - 15)\)[/tex] is:
[tex]\[
(5x - 3)(4x + 5)
\][/tex]
Therefore, the final answer is:
[tex]\[
(5x - 3)(4x + 5)
\][/tex]
