Solve (3c+4)(2c+5)

Question

Simplify the expression

6 c^{2} + 23 c + 20

Evaluate

(3 c + 4) (2 c + 5)

Apply the distributive property

3 c \times 2 c + 3 c \times 5 + 4 \times 2 c + 4 \times 5

Multiply the terms

More Steps

Evaluate

3 c \times 2 c

Multiply the numbers

6 c \times c

Multiply the terms

6 c^{2}

6 c^{2} + 3 c \times 5 + 4 \times 2 c + 4 \times 5

Multiply the numbers

6 c^{2} + 15 c + 4 \times 2 c + 4 \times 5

Multiply the numbers

6 c^{2} + 15 c + 8 c + 4 \times 5

Multiply the numbers

6 c^{2} + 15 c + 8 c + 20

Solution

More Steps

Evaluate

15 c + 8 c

Collect like terms by calculating the sum or difference of their coefficients

(15 + 8) c

Add the numbers

23 c

6 c^{2} + 23 c + 20

Show Solution

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

Alternative Form

c_{1} = - 2.5, c_{2} = - 1. \dot{3}

Evaluate

(3 c + 4) (2 c + 5)

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

(3 c + 4) (2 c + 5) = 0

Separate the equation into 2 possible cases

3 c + 4 = 0 2 c + 5 = 0

Solve the equation

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}

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

c = - \frac{4}{3}

c = - \frac{4}{3} 2 c + 5 = 0

Solve the equation

More Steps

Evaluate

2 c + 5 = 0

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

2 c = 0 - 5

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

2 c = - 5

Divide both sides

\frac{2 c}{2} = \frac{- 5}{2}

Divide the numbers

c = \frac{- 5}{2}

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

c = - \frac{5}{2}

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

Solution

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

Alternative Form

c_{1} = - 2.5, c_{2} = - 1. \dot{3}

Show Solution