Solve 12x^2-32x=0;12x-32=0

Question

Solve the system of equations

x = \frac{8}{3}

Alternative Form

x = 2. \dot{6}

Evaluate

{12 x^{2} - 32 x = 0 12 x - 32 = 0

Calculate

More Steps

Evaluate

12 x^{2} - 32 x = 0

Factor the expression

More Steps

Evaluate

12 x^{2} - 32 x

Rewrite the expression

4 x \times 3 x - 4 x \times 8

Factor out 4 x from the expression

4 x (3 x - 8)

4 x (3 x - 8) = 0

When the product of factors equals 0,at least one factor is 0

4 x = 0 3 x - 8 = 0

Solve the equation for x

x = 0 3 x - 8 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 8 = 0

Move the constant to the right-hand side and change its sign

3 x = 0 + 8

Removing 0 doesn't change the value,so remove it from the expression

3 x = 8

Divide both sides

\frac{3 x}{3} = \frac{8}{3}

Divide the numbers

x = \frac{8}{3}

x = 0 x = \frac{8}{3}

Calculate

x = 0 \cup x = \frac{8}{3}

{x = 0 \cup x = \frac{8}{3} 12 x - 32 = 0

Calculate

More Steps

Evaluate

12 x - 32 = 0

Move the constant to the right-hand side and change its sign

12 x = 0 + 32

Removing 0 doesn't change the value,so remove it from the expression

12 x = 32

Divide both sides

\frac{12 x}{12} = \frac{32}{12}

Divide the numbers

x = \frac{32}{12}

Cancel out the common factor 4

x = \frac{8}{3}

{x = 0 \cup x = \frac{8}{3} x = \frac{8}{3}

Find the intersection

x = \frac{8}{3}

Solution

More Steps

Check the solution

{12 (\frac{8}{3})^{2} - 32 \times \frac{8}{3} = 0 12 \times \frac{8}{3} - 32 = 0

Simplify

{0 = 0 0 = 0

Evaluate

true

x = \frac{8}{3}

Alternative Form

x = 2. \dot{6}

Show Solution