Solve for x 3b(2x-a^2)=5d-7gx

$3 b (2 x - a^{2}) = 5 d - 7 g x$

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

Rewrite.

$0 + 0 + 3 b (2 x - a^{2}) = 5 d - 7 g x$

Simplify by multiplying through.

Apply the distributive property.

$3 b (2 x) + 3 b (- a^{2}) = 5 d - 7 g x$

Reorder.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 b x + 3 b (- a^{2}) = 5 d - 7 g x$

Rewrite using the commutative property of multiplication.

$3 \cdot 2 b x + 3 \cdot - 1 b a^{2} = 5 d - 7 g x$

Simplify each term.

Multiply $3$ by $2$ .

$6 b x + 3 \cdot - 1 b a^{2} = 5 d - 7 g x$

Multiply $3$ by $- 1$ .

$6 b x - 3 b a^{2} = 5 d - 7 g x$

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

$6 b x - 3 b a^{2} + 7 g x = 5 d$

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

$6 b x + 7 g x = 5 d + 3 b a^{2}$

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

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

$x (6 b) + 7 g x = 5 d + 3 b a^{2}$

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

$x (6 b) + x (7 g) = 5 d + 3 b a^{2}$

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

$x (6 b + 7 g) = 5 d + 3 b a^{2}$

Divide each term in $x (6 b + 7 g) = 5 d + 3 b a^{2}$ by $6 b + 7 g$ and simplify.

Divide each term in $x (6 b + 7 g) = 5 d + 3 b a^{2}$ by $6 b + 7 g$ .

$\frac{x (6 b + 7 g)}{6 b + 7 g} = \frac{5 d}{6 b + 7 g} + \frac{3 b a^{2}}{6 b + 7 g}$

Simplify the left side.

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

Cancel the common factor.

$\frac{x (6 b + 7 g)}{6 b + 7 g} = \frac{5 d}{6 b + 7 g} + \frac{3 b a^{2}}{6 b + 7 g}$

Divide $x$ by $1$ .

$x = \frac{5 d}{6 b + 7 g} + \frac{3 b a^{2}}{6 b + 7 g}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{5 d + 3 b a^{2}}{6 b + 7 g}$