Let's solve the equation:
3(4x^2 )=(5x−3)(7x)
We can solve the equation by multiplying, re-ordering terms, distributing, combining like terms, factoring, dividing both sides of the equation by the same factor, using the quadratic formula, and simplifying.
Steps to solve:
1. Multiply the numbers:
12x^2 =(5x−3)(7x)
2. Re-order terms so constants are on the left:
12x^2 =7(5x−3)x
3. Distribute:
12x^2 =35x^2 −21x
4. Move terms to the left side:
12x^2 −(35x^2 −21x)=0
5. Distribute:
12x^2 −35x^2 +21x=0
6. Combine like terms:
−23x^2 +21x=0
7. Factor:
−(23x^2 −21x)=0
8. Divide both sides of the equation by the same factor:
23x^2 −21x=0
9. Use the quadratic formula:
x= −b± √b^2 −4ac/ 2a
Quadratic formula coefficient plug-in.
x= 21±21/46
11. Separate the equations:
x= 21/23
x=0