Solve 71f(-5x+(2x+3))=25-(-(3x+4)-(4x+3))

$$71 f ( - 5 x + ( 2 x + 3 ) ) = 25 - ( - ( 3 x + 4 ) - ( 4 x + 3 ) )$$

Solve for f

$$f=\frac{7x+32}{213\left(1-x\right)}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Combine -5x and 2x to get -3x.

$$71f\left(-3x+3\right)=25-\left(-\left(3x+4\right)-\left(4x+3\right)\right)$$

Use the distributive property to multiply 71f by -3x+3.

$$-213fx+213f=25-\left(-\left(3x+4\right)-\left(4x+3\right)\right)$$

To find the opposite of 3x+4, find the opposite of each term.

$$-213fx+213f=25-\left(-3x-4-\left(4x+3\right)\right)$$

To find the opposite of 4x+3, find the opposite of each term.

$$-213fx+213f=25-\left(-3x-4-4x-3\right)$$

Combine -3x and -4x to get -7x.

$$-213fx+213f=25-\left(-7x-4-3\right)$$

Subtract 3 from -4 to get -7.

$$-213fx+213f=25-\left(-7x-7\right)$$

To find the opposite of -7x-7, find the opposite of each term.

$$-213fx+213f=25+7x+7$$

Add 25 and 7 to get 32.

$$-213fx+213f=32+7x$$

Combine all terms containing f.

$$\left(-213x+213\right)f=32+7x$$

The equation is in standard form.

$$\left(213-213x\right)f=7x+32$$

Divide both sides by -213x+213.

$$\frac{\left(213-213x\right)f}{213-213x}=\frac{7x+32}{213-213x}$$

Dividing by -213x+213 undoes the multiplication by -213x+213.

$$f=\frac{7x+32}{213-213x}$$

Divide 32+7x by -213x+213.

$$f=\frac{7x+32}{213\left(1-x\right)}$$

Solve for x

$$x=\frac{213f-32}{213f+7}$$

$$f\neq -\frac{7}{213}$$

Steps for Solving Linear Equation

Combine -5x and 2x to get -3x.

$$71f\left(-3x+3\right)=25-\left(-\left(3x+4\right)-\left(4x+3\right)\right)$$

Use the distributive property to multiply 71f by -3x+3.

$$-213xf+213f=25-\left(-\left(3x+4\right)-\left(4x+3\right)\right)$$

To find the opposite of 3x+4, find the opposite of each term.

$$-213xf+213f=25-\left(-3x-4-\left(4x+3\right)\right)$$

To find the opposite of 4x+3, find the opposite of each term.

$$-213xf+213f=25-\left(-3x-4-4x-3\right)$$

Combine -3x and -4x to get -7x.

$$-213xf+213f=25-\left(-7x-4-3\right)$$

Subtract 3 from -4 to get -7.

$$-213xf+213f=25-\left(-7x-7\right)$$

To find the opposite of -7x-7, find the opposite of each term.

$$-213xf+213f=25+7x+7$$

Add 25 and 7 to get 32.

$$-213xf+213f=32+7x$$

Subtract 7x from both sides.

$$-213xf+213f-7x=32$$

Subtract 213f from both sides.

$$-213xf-7x=32-213f$$

Combine all terms containing x.

$$\left(-213f-7\right)x=32-213f$$

Divide both sides by -213f-7.

$$\frac{\left(-213f-7\right)x}{-213f-7}=\frac{32-213f}{-213f-7}$$

Dividing by -213f-7 undoes the multiplication by -213f-7.

$$x=\frac{32-213f}{-213f-7}$$

Divide 32-213f by -213f-7.

$$x=-\frac{32-213f}{213f+7}$$