Solve 6x^2-3-7x - ScanMath

Question

Factor the expression

(2 x - 3) (3 x + 1)

Evaluate

6 x^{2} - 3 - 7 x

Reorder the terms

6 x^{2} - 7 x - 3

Rewrite the expression

6 x^{2} + (2 - 9) x - 3

Calculate

6 x^{2} + 2 x - 9 x - 3

Rewrite the expression

2 x \times 3 x + 2 x - 3 \times 3 x - 3

Factor out 2 x from the expression

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

Factor out - 3 from the expression

2 x (3 x + 1) - 3 (3 x + 1)

Solution

(2 x - 3) (3 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 1.5

Evaluate

6 x^{2} - 3 - 7 x

To find the roots of the expression,set the expression equal to 0

6 x^{2} - 3 - 7 x = 0

Factor the expression

More Steps

Evaluate

6 x^{2} - 3 - 7 x

Reorder the terms

6 x^{2} - 7 x - 3

Rewrite the expression

6 x^{2} + (2 - 9) x - 3

Calculate

6 x^{2} + 2 x - 9 x - 3

Rewrite the expression

2 x \times 3 x + 2 x - 3 \times 3 x - 3

Factor out 2 x from the expression

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

Factor out - 3 from the expression

2 x (3 x + 1) - 3 (3 x + 1)

Factor out 3 x + 1 from the expression

(2 x - 3) (3 x + 1)

(2 x - 3) (3 x + 1) = 0

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

2 x - 3 = 0 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

\frac{2 x}{2} = \frac{3}{2}

Divide the numbers

x = \frac{3}{2}

x = \frac{3}{2} 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}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{3}

x = \frac{3}{2} x = - \frac{1}{3}

Solution

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 1.5

Show Solution