4(2x -3) -37 = 5 (4-3x) => 8x - 12 -37 = 20- 15x => 8x -49 = 20-15x => 8x + 15x = 20+49 => 23x = 69 => x = 69 /23 => x=3

Given equation: 4(2x-3)-37=5(4-3x)

To solve this equation, we will follow the order of operations (PEMDAS) and simplify the expression on both sides of the equation.

Distributive Property:
On the left side of the equation, we can distribute the 4 to the terms inside the parentheses:
4 * 2x = 8x
4 * -3 = -12
Therefore, the left side simplifies to 8x - 12.

On the right side of the equation, we can distribute the 5 to the terms inside the parentheses:
5 * 4 = 20
5 * -3x = -15x
Therefore, the right side simplifies to 20 - 15x.

Combining Like Terms:
Now we can combine the like terms on both sides of the equation:
8x - 12 - 37 = 20 - 15x

Subtraction:
We can subtract 12 from -37 on the left side of the equation:
8x - 49 = 20 - 15x

Addition:
Next, we can add 15x to both sides of the equation to eliminate the variable term on the right side:
8x + 15x - 49 = 20 - 15x + 15x
23x - 49 = 20

Addition:
Now, we can add 49 to both sides of the equation to isolate the variable term on the left side:
23x - 49 + 49 = 20 + 49
23x = 69

Division:
Finally, we can divide both sides of the equation by 23 to solve for x:
23x/23 = 69/23
x = 3

Solution:
Therefore, the solution to the equation 4(2x-3)-37=5(4-3x) is x = 3.