Solve 15c^2 -c-20= 3c^2

Question

Solve the quadratic equation

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

Alternative Form

c_{1} = - 1.25, c_{2} = 1. \dot{3}

Evaluate

15 c^{2} - c - 20 = 3 c^{2}

Move the expression to the left side

12 c^{2} - c - 20 = 0

Factor the expression

More Steps

Evaluate

12 c^{2} - c - 20

Rewrite the expression

12 c^{2} + (15 - 16) c - 20

Calculate

12 c^{2} + 15 c - 16 c - 20

Rewrite the expression

3 c \times 4 c + 3 c \times 5 - 4 \times 4 c - 4 \times 5

Factor out 3 c from the expression

3 c (4 c + 5) - 4 \times 4 c - 4 \times 5

Factor out - 4 from the expression

3 c (4 c + 5) - 4 (4 c + 5)

Factor out 4 c + 5 from the expression

(3 c - 4) (4 c + 5)

(3 c - 4) (4 c + 5) = 0

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

3 c - 4 = 0 4 c + 5 = 0

Solve the equation for c

More Steps

Evaluate

3 c - 4 = 0

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

3 c = 0 + 4

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

3 c = 4

Divide both sides

\frac{3 c}{3} = \frac{4}{3}

Divide the numbers

c = \frac{4}{3}

c = \frac{4}{3} 4 c + 5 = 0

Solve the equation for c

More Steps

Evaluate

4 c + 5 = 0

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

4 c = 0 - 5

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

4 c = - 5

Divide both sides

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

Divide the numbers

c = \frac{- 5}{4}

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

c = - \frac{5}{4}

c = \frac{4}{3} c = - \frac{5}{4}

Solution

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

Alternative Form

c_{1} = - 1.25, c_{2} = 1. \dot{3}

Show Solution