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

Question

Simplify the expression

Solution

12 f^{2} + 26 f + 10

Evaluate

(4 f + 2) (3 f + 5)

Apply the distributive property

4 f \times 3 f + 4 f \times 5 + 2 \times 3 f + 2 \times 5

Multiply the terms

More Steps

Evaluate

4 f \times 3 f

Multiply the numbers

12 f \times f

Multiply the terms

12 f^{2}

12 f^{2} + 4 f \times 5 + 2 \times 3 f + 2 \times 5

Multiply the numbers

12 f^{2} + 20 f + 2 \times 3 f + 2 \times 5

Multiply the numbers

12 f^{2} + 20 f + 6 f + 2 \times 5

Multiply the numbers

12 f^{2} + 20 f + 6 f + 10

Solution

More Steps

Evaluate

20 f + 6 f

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

(20 + 6) f

Add the numbers

26 f

12 f^{2} + 26 f + 10

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Factor the expression

Factor

2 (2 f + 1) (3 f + 5)

Evaluate

(4 f + 2) (3 f + 5)

Solution

2 (2 f + 1) (3 f + 5)

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Find the roots

Find the roots of the algebra expression

f_{1} = - \frac{5}{3}, f_{2} = - \frac{1}{2}

Alternative Form

f_{1} = - 1. \dot{6}, f_{2} = - 0.5

Evaluate

(4 f + 2) (3 f + 5)

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

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

Separate the equation into 2 possible cases

4 f + 2 = 0 3 f + 5 = 0

Solve the equation

More Steps

Evaluate

4 f + 2 = 0

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

4 f = 0 - 2

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

4 f = - 2

Divide both sides

\frac{4 f}{4} = \frac{- 2}{4}

Divide the numbers

f = \frac{- 2}{4}

Divide the numbers

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Evaluate

\frac{- 2}{4}

Cancel out the common factor 2

\frac{- 1}{2}

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

- \frac{1}{2}

f = - \frac{1}{2}

f = - \frac{1}{2} 3 f + 5 = 0

Solve the equation

More Steps

Evaluate

3 f + 5 = 0

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

3 f = 0 - 5

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

3 f = - 5

Divide both sides

\frac{3 f}{3} = \frac{- 5}{3}

Divide the numbers

f = \frac{- 5}{3}

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

f = - \frac{5}{3}

f = - \frac{1}{2} f = - \frac{5}{3}

Solution

f_{1} = - \frac{5}{3}, f_{2} = - \frac{1}{2}

Alternative Form

f_{1} = - 1. \dot{6}, f_{2} = - 0.5

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