5x-(2a^6•16b)= -3b(6a^2 -(5bx))
To solve the equation 5x - (2a^6 * 16b) = -3b(6a^2 - (5bx)), we'll start by simplifying each side of the equation separately.
Let's simplify the left side first:
5x - (2a^6 * 16b)
Step 1: Simplify the expression within parentheses:
2a^6 * 16b = 32a^6b
Substituting this back into the original equation:
5x - 32a^6b
Now, let's simplify the right side of the equation:
-3b(6a^2 - (5bx))
Step 1: Distribute the -3b to each term within the parentheses:
-3b * 6a^2 = -18a^2b
-3b * (-5bx) = 15bx^2
Substituting these results back into the original equation:
-18a^2b + 15bx^2
Therefore, the original equation simplifies to:
5x - 32a^6b = -18a^2b + 15bx^2
To continue solving this equation, we need to collect all the terms with "x" on one side, and all the terms without "x" on the other side.
Let's rearrange the equation by moving terms:
5x - 15bx^2 = -18a^2b + 32a^6b
Now, factor out the "x" and "b" from each side:
x(5 - 15bx) = b(-18a^2 + 32a^6)
To find the values of "x" and "b," we will set each factor equal to zero:
5 - 15bx = 0 (equation 1)
-18a^2 + 32a^6 = 0 (equation 2)
Now, let's solve equation 1 for "x":
5 - 15bx = 0
Step 1: Move 5 to the other side of the equation:
-15bx = -5
Step 2: Divide both sides by -15b:
x = -5 / -15b
Simplifying the equation:
x = 1 / 3b
Next, let's solve equation 2 for "a":
-18a^2 + 32a^6 = 0
Step 1: Factor out "a^2":
a^2 * (-18 + 32a^4) = 0
To find the values of "a," we'll solve the equation a^2 = 0 separately and then solve -18 + 32a^4 = 0 separately:
Solving a^2 = 0:
a^2 = 0
a = 0
Solving -18 + 32a^4 = 0:
-18 + 32a^4 = 0
Step 1: Add 18 to both sides of the equation:
32a^4 = 18
Step 2: Divide both sides by 32:
a^4 = 18/32
Step 3: Simplify the right side of the equation:
a^4 = 9/16
Step 4: Take the fourth root of both sides to solve for "a":
a = ±√(9/16)
Simplifying the equation:
a = ±(3/4)
So, the solutions to the equation 5x - (2a^6 * 16b) = -3b(6a^2 - (5bx)) are:
x = 1 / 3b
a = ±(3/4)
Remember to check any restrictions on the variables to ensure they are valid solutions for the specific problem or context.