Solve for c -0.1(90c+5)=2.5(-1.4-3c)

$- 0.1 (90 c + 5) = 2.5 (- 1.4 - 3 c)$

Step 1

Simplify $- 0.1 (90 c + 5)$ .

Rewrite.

$0 + 0 - 0.1 (90 c + 5) = 2.5 (- 1.4 - 3 c)$

Simplify by adding zeros.

$- 0.1 (90 c + 5) = 2.5 (- 1.4 - 3 c)$

Apply the distributive property.

$- 0.1 (90 c) - 0.1 \cdot 5 = 2.5 (- 1.4 - 3 c)$

Multiply.

Multiply $90$ by $- 0.1$ .

$- 9 c - 0.1 \cdot 5 = 2.5 (- 1.4 - 3 c)$

Multiply $- 0.1$ by $5$ .

$- 9 c - 0.5 = 2.5 (- 1.4 - 3 c)$

Step 2

Simplify $2.5 (- 1.4 - 3 c)$ .

Apply the distributive property.

$- 9 c - 0.5 = 2.5 \cdot - 1.4 + 2.5 (- 3 c)$

Multiply.

Multiply $2.5$ by $- 1.4$ .

$- 9 c - 0.5 = - 3.5 + 2.5 (- 3 c)$

Multiply $- 3$ by $2.5$ .

$- 9 c - 0.5 = - 3.5 - 7.5 c$

Step 3

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

Add $7.5 c$ to both sides of the equation.

$- 9 c - 0.5 + 7.5 c = - 3.5$

Add $- 9 c$ and $7.5 c$ .

$- 1.5 c - 0.5 = - 3.5$

Step 4

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

Add $0.5$ to both sides of the equation.

$- 1.5 c = - 3.5 + 0.5$

Add $- 3.5$ and $0.5$ .

$- 1.5 c = - 3$

Step 5

Divide each term in $- 1.5 c = - 3$ by $- 1.5$ and simplify.

Divide each term in $- 1.5 c = - 3$ by $- 1.5$ .

$\frac{- 1.5 c}{- 1.5} = \frac{- 3}{- 1.5}$

Simplify the left side.

Cancel the common factor of $- 1.5$ .

Cancel the common factor.

$\frac{- 1.5 c}{- 1.5} = \frac{- 3}{- 1.5}$

Divide $c$ by $1$ .

$c = \frac{- 3}{- 1.5}$

Simplify the right side.

Divide $- 3$ by $- 1.5$ .

$c = 2$

Solve for c -0.1(90c+5)=2.5(-1.4-3c)

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