Basic Math Examples

$3 (3 - c) - 33 = 27 c - 6 (4 + 5 c)$

Step 1

Since $c$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$27 c - 6 (4 + 5 c) = 3 (3 - c) - 33$

Step 2

Simplify $27 c - 6 (4 + 5 c)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$27 c - 6 \cdot 4 - 6 (5 c) = 3 (3 - c) - 33$

Step 2.1.2

Multiply $- 6$ by $4$ .

$27 c - 24 - 6 (5 c) = 3 (3 - c) - 33$

Step 2.1.3

Multiply $5$ by $- 6$ .

$27 c - 24 - 30 c = 3 (3 - c) - 33$

Step 2.2

Subtract $30 c$ from $27 c$ .

$- 3 c - 24 = 3 (3 - c) - 33$

Step 3

Simplify $3 (3 - c) - 33$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 3 c - 24 = 3 \cdot 3 + 3 (- c) - 33$

Step 3.1.2

Multiply $3$ by $3$ .

$- 3 c - 24 = 9 + 3 (- c) - 33$

Step 3.1.3

Multiply $- 1$ by $3$ .

$- 3 c - 24 = 9 - 3 c - 33$

Step 3.2

Subtract $33$ from $9$ .

$- 3 c - 24 = - 3 c - 24$

Step 4

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

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Step 4.1

Add $3 c$ to both sides of the equation.

$- 3 c - 24 + 3 c = - 24$

Step 4.2

Combine the opposite terms in $- 3 c - 24 + 3 c$ .

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Step 4.2.1

Add $- 3 c$ and $3 c$ .

$0 - 24 = - 24$

Step 4.2.2

Subtract $24$ from $0$ .

$- 24 = - 24$

Step 5

Since $- 24 = - 24$ , the equation will always be true for any value of $c$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$