Algebra Examples

$3 b (2 x - a^{2}) = 2 h - 7 g x$

Step 1

Simplify $3 b (2 x - a^{2})$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 b (2 x - a^{2}) = 2 h - 7 g x$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$3 b (2 x) + 3 b (- a^{2}) = 2 h - 7 g x$

Step 1.2.2

Reorder.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 2 b x + 3 b (- a^{2}) = 2 h - 7 g x$

Step 1.2.2.2

Rewrite using the commutative property of multiplication.

$3 \cdot 2 b x + 3 \cdot - 1 b a^{2} = 2 h - 7 g x$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $3$ by $2$ .

$6 b x + 3 \cdot - 1 b a^{2} = 2 h - 7 g x$

Step 1.3.2

Multiply $3$ by $- 1$ .

$6 b x - 3 b a^{2} = 2 h - 7 g x$

Step 2

Add $7 g x$ to both sides of the equation.

$6 b x - 3 b a^{2} + 7 g x = 2 h$

Step 3

Add $3 b a^{2}$ to both sides of the equation.

$6 b x + 7 g x = 2 h + 3 b a^{2}$

Step 4

Factor $x$ out of $6 b x + 7 g x$ .

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Step 4.1

Factor $x$ out of $6 b x$ .

$x (6 b) + 7 g x = 2 h + 3 b a^{2}$

Step 4.2

Factor $x$ out of $7 g x$ .

$x (6 b) + x (7 g) = 2 h + 3 b a^{2}$

Step 4.3

Factor $x$ out of $x (6 b) + x (7 g)$ .

$x (6 b + 7 g) = 2 h + 3 b a^{2}$

Step 5

Divide each term in $x (6 b + 7 g) = 2 h + 3 b a^{2}$ by $6 b + 7 g$ and simplify.

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Step 5.1

Divide each term in $x (6 b + 7 g) = 2 h + 3 b a^{2}$ by $6 b + 7 g$ .

$\frac{x (6 b + 7 g)}{6 b + 7 g} = \frac{2 h}{6 b + 7 g} + \frac{3 b a^{2}}{6 b + 7 g}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6 b + 7 g$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x (6 b + 7 g)}{6 b + 7 g} = \frac{2 h}{6 b + 7 g} + \frac{3 b a^{2}}{6 b + 7 g}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{2 h}{6 b + 7 g} + \frac{3 b a^{2}}{6 b + 7 g}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

$x = \frac{2 h + 3 b a^{2}}{6 b + 7 g}$