Multiply:- 4a^2 - 6a + 5 by 3a + 2.
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4a^2 + 9a + 10

Step-by-step explanation:

First we distribute

-4a^2 + (−6a) + (5)(3a) + (5)(2)

-4a^2 - 6a + 15a + 10

Then we combine like terms

4a^2 has no like terms, so it cannot be added onto anything else.

We add -6a to 15a

15a - 6a = 9a

4a^2 + 9a + 10

Simplifying

(6a + -8)(4a2) = 0

Reorder the terms:

(-8 + 6a)(4a2) = 0

Remove parenthesis around (4a2)

(-8 + 6a) * 4a2 = 0

Reorder the terms for easier multiplication:

4a2(-8 + 6a) = 0

(-8 * 4a2 + 6a * 4a2) = 0

(-32a2 + 24a3) = 0

Solving

-32a2 + 24a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8a2'.

8a2(-4 + 3a) = 0

Ignore the factor 8.

Subproblem 1

Set the factor 'a2' equal to zero and attempt to solve:

Simplifying

a2 = 0

Solving

a2 = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying

a2 = 0

Take the square root of each side:

a = {0}

Subproblem 2

Set the factor '(-4 + 3a)' equal to zero and attempt to solve:

Simplifying

-4 + 3a = 0

Solving

-4 + 3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '4' to each side of the equation.

-4 + 4 + 3a = 0 + 4

Combine like terms: -4 + 4 = 0

0 + 3a = 0 + 4

3a = 0 + 4

Combine like terms: 0 + 4 = 4

3a = 4

Divide each side by '3'.

a = 1.333333333

Simplifying

a = 1.333333333

Solution

a = {0, 1.333333333}

Step-by-step explanation: