Solve 3x^2 -32x+13=-10x+6

Question

Solve the quadratic equation

x_{1} = \frac{1}{3}, x_{2} = 7

Alternative Form

x_{1} = 0. \dot{3}, x_{2} = 7

Evaluate

3 x^{2} - 32 x + 13 = - 10 x + 6

Move the expression to the left side

3 x^{2} - 22 x + 7 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 22 x + 7

Rewrite the expression

3 x^{2} + (- 1 - 21) x + 7

Calculate

3 x^{2} - x - 21 x + 7

Rewrite the expression

x \times 3 x - x - 7 \times 3 x + 7

Factor out x from the expression

x (3 x - 1) - 7 \times 3 x + 7

Factor out - 7 from the expression

x (3 x - 1) - 7 (3 x - 1)

Factor out 3 x - 1 from the expression

(x - 7) (3 x - 1)

(x - 7) (3 x - 1) = 0

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

x - 7 = 0 3 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 7 = 0

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

x = 0 + 7

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

x = 7

x = 7 3 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 1 = 0

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

3 x = 0 + 1

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

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = 7 x = \frac{1}{3}

Solution

x_{1} = \frac{1}{3}, x_{2} = 7

Alternative Form

x_{1} = 0. \dot{3}, x_{2} = 7

Show Solution