Solve for u (100-4u)/3=(5u+6)/4+6

$\frac{100 - 4 u}{3} = \frac{5 u + 6}{4} + 6$

Multiply both sides by $3$ .

$\frac{100 - 4 u}{3} \cdot 3 = (\frac{5 u + 6}{4} + 6) \cdot 3$

Simplify.

Simplify the left side.

Simplify $\frac{100 - 4 u}{3} \cdot 3$ .

Factor $4$ out of $100 - 4 u$ .

Factor $4$ out of $100$ .

$\frac{4 (25) - 4 u}{3} \cdot 3 = (\frac{5 u + 6}{4} + 6) \cdot 3$

Factor $4$ out of $- 4 u$ .

$\frac{4 (25) + 4 (- u)}{3} \cdot 3 = (\frac{5 u + 6}{4} + 6) \cdot 3$

Factor $4$ out of $4 (25) + 4 (- u)$ .

$\frac{4 (25 - u)}{3} \cdot 3 = (\frac{5 u + 6}{4} + 6) \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4 (25 - u)}{3} \cdot 3 = (\frac{5 u + 6}{4} + 6) \cdot 3$

Rewrite the expression.

$4 (25 - u) = (\frac{5 u + 6}{4} + 6) \cdot 3$

Apply the distributive property.

$4 \cdot 25 + 4 (- u) = (\frac{5 u + 6}{4} + 6) \cdot 3$

Simplify the expression.

Multiply $4$ by $25$ .

$100 + 4 (- u) = (\frac{5 u + 6}{4} + 6) \cdot 3$

Multiply $- 1$ by $4$ .

$100 - 4 u = (\frac{5 u + 6}{4} + 6) \cdot 3$

Reorder $100$ and $- 4 u$ .

$- 4 u + 100 = (\frac{5 u + 6}{4} + 6) \cdot 3$

Simplify the right side.

Simplify $(\frac{5 u + 6}{4} + 6) \cdot 3$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 4 u + 100 = (\frac{5 u + 6}{4} + 6 \cdot \frac{4}{4}) \cdot 3$

Simplify terms.

Combine $6$ and $\frac{4}{4}$ .

$- 4 u + 100 = (\frac{5 u + 6}{4} + \frac{6 \cdot 4}{4}) \cdot 3$

Combine the numerators over the common denominator.

$- 4 u + 100 = \frac{5 u + 6 + 6 \cdot 4}{4} \cdot 3$

Simplify the numerator.

Multiply $6$ by $4$ .

$- 4 u + 100 = \frac{5 u + 6 + 24}{4} \cdot 3$

Add $6$ and $24$ .

$- 4 u + 100 = \frac{5 u + 30}{4} \cdot 3$

Factor $5$ out of $5 u + 30$ .

Factor $5$ out of $5 u$ .

$- 4 u + 100 = \frac{5 (u) + 30}{4} \cdot 3$

Factor $5$ out of $30$ .

$- 4 u + 100 = \frac{5 u + 5 \cdot 6}{4} \cdot 3$

Factor $5$ out of $5 u + 5 \cdot 6$ .

$- 4 u + 100 = \frac{5 (u + 6)}{4} \cdot 3$

Multiply $\frac{5 (u + 6)}{4} \cdot 3$ .

Combine $\frac{5 (u + 6)}{4}$ and $3$ .

$- 4 u + 100 = \frac{5 (u + 6) \cdot 3}{4}$

Multiply $3$ by $5$ .

$- 4 u + 100 = \frac{15 (u + 6)}{4}$

Solve for $u$ .

Multiply both sides by $4$ .

$(- 4 u + 100) \cdot 4 = \frac{15 (u + 6)}{4} \cdot 4$

Simplify.

Simplify the left side.

Simplify $(- 4 u + 100) \cdot 4$ .

Apply the distributive property.

$- 4 u \cdot 4 + 100 \cdot 4 = \frac{15 (u + 6)}{4} \cdot 4$

Multiply.

Multiply $4$ by $- 4$ .

$- 16 u + 100 \cdot 4 = \frac{15 (u + 6)}{4} \cdot 4$

Multiply $100$ by $4$ .

$- 16 u + 400 = \frac{15 (u + 6)}{4} \cdot 4$

Simplify the right side.

Simplify $\frac{15 (u + 6)}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$- 16 u + 400 = \frac{15 (u + 6)}{4} \cdot 4$

Rewrite the expression.

$- 16 u + 400 = 15 (u + 6)$

Apply the distributive property.

$- 16 u + 400 = 15 u + 15 \cdot 6$

Multiply $15$ by $6$ .

$- 16 u + 400 = 15 u + 90$

Solve for $u$ .

Move all terms containing $u$ to the left side of the equation.

Subtract $15 u$ from both sides of the equation.

$- 16 u + 400 - 15 u = 90$

Subtract $15 u$ from $- 16 u$ .

$- 31 u + 400 = 90$

Move all terms not containing $u$ to the right side of the equation.

Subtract $400$ from both sides of the equation.

$- 31 u = 90 - 400$

Subtract $400$ from $90$ .

$- 31 u = - 310$

Divide each term in $- 31 u = - 310$ by $- 31$ and simplify.

Divide each term in $- 31 u = - 310$ by $- 31$ .

$\frac{- 31 u}{- 31} = \frac{- 310}{- 31}$

Simplify the left side.

Cancel the common factor of $- 31$ .

Cancel the common factor.

$\frac{- 31 u}{- 31} = \frac{- 310}{- 31}$

Divide $u$ by $1$ .

$u = \frac{- 310}{- 31}$

Simplify the right side.

Divide $- 310$ by $- 31$ .

$u = 10$

Solve for u (100-4u)/3=(5u+6)/4+6

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