Solve for x: 28 + 16x + 45 * 0.92 * (4 - 2x) + 350 * (4 - 2x) * 0.08 = 152.0621.

Step-by-step solution

1. 1

   Simplify the two numeric coefficients. Before touching the brackets, evaluate what multiplies each one:

   $45\cdot 0.92=41.4,\qquad 350\cdot 0.08=28$

2. 2

   Combine the shared factor $4-2x$. Both terms carry the same bracket, so they merge:

   $41.4(4-2x)+28(4-2x)=(41.4+28)(4-2x)=69.4(4-2x)$

   Spotting the common factor first avoids expanding two separate products and halves the arithmetic.

3. 3

   Expand and collect.

   $28+16x+277.6-138.8x=152.0621$

   $305.6-122.8x=152.0621$

   The $x$ coefficient is $16-138.8=-122.8$, so the left side decreases as $x$ grows.

4. 4

   Solve for $x$.

   $122.8x=305.6-152.0621=153.5379\;\Longrightarrow\;x=\frac{153.5379}{122.8}\approx 1.25031$

5. 5

   Check by substitution. With $x=1.2503086$: $4-2x=1.4993828$, so $69.4(1.4993828)=104.0572$ and $16x=20.0049$. Adding the leading $28$:

   $28+20.0049+104.0572=152.0621\;\checkmark$

   Note the bracket $4-2x$ stays positive, which matters if it represents a remaining quantity in the underlying application.