Solve 10x^2-7x-12

Question

Factor the expression

(2 x - 3) (5 x + 4)

Evaluate

10 x^{2} - 7 x - 12

Rewrite the expression

10 x^{2} + (8 - 15) x - 12

Calculate

10 x^{2} + 8 x - 15 x - 12

Rewrite the expression

2 x \times 5 x + 2 x \times 4 - 3 \times 5 x - 3 \times 4

Factor out 2 x from the expression

2 x (5 x + 4) - 3 \times 5 x - 3 \times 4

Factor out - 3 from the expression

2 x (5 x + 4) - 3 (5 x + 4)

Solution

(2 x - 3) (5 x + 4)

Show Solution

x_{1} = - \frac{4}{5}, x_{2} = \frac{3}{2}

Alternative Form

x_{1} = - 0.8, x_{2} = 1.5

Evaluate

10 x^{2} - 7 x - 12

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

10 x^{2} - 7 x - 12 = 0

Factor the expression

More Steps

Evaluate

10 x^{2} - 7 x - 12

Rewrite the expression

10 x^{2} + (8 - 15) x - 12

Calculate

10 x^{2} + 8 x - 15 x - 12

Rewrite the expression

2 x \times 5 x + 2 x \times 4 - 3 \times 5 x - 3 \times 4

Factor out 2 x from the expression

2 x (5 x + 4) - 3 \times 5 x - 3 \times 4

Factor out - 3 from the expression

2 x (5 x + 4) - 3 (5 x + 4)

Factor out 5 x + 4 from the expression

(2 x - 3) (5 x + 4)

(2 x - 3) (5 x + 4) = 0

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

2 x - 3 = 0 5 x + 4 = 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} 5 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 4 = 0

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

5 x = 0 - 4

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

5 x = - 4

Divide both sides

\frac{5 x}{5} = \frac{- 4}{5}

Divide the numbers

x = \frac{- 4}{5}

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

x = - \frac{4}{5}

x = \frac{3}{2} x = - \frac{4}{5}

Solution

x_{1} = - \frac{4}{5}, x_{2} = \frac{3}{2}

Alternative Form

x_{1} = - 0.8, x_{2} = 1.5

Show Solution