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Hi there!

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Let's solve for c.

[tex]\left(5x\ +\ 4\right)\left(2x\ +\ c\right)\ =\ 10x^{2\ }+\ nx\ -\ 12[/tex]

Step 1: Add [tex]-10x^2[/tex] to both sides.

[tex]5cx + 10x^2 + 4c + 8x + -10x^2 = nx + 10^2 - 12 + -10x^2[/tex]

[tex]5cx + 4c + 8x = nx - 12[/tex]

Step 2: Add [tex]-8x[/tex] to both sides.

[tex]5cx + 4c + 8x + -8x = nx - 12 + -8x[/tex]

[tex]5cx + 4c = nx - 8x - 12[/tex]

Step 3: Factor out variable c.

[tex]c(5x + 4) = nx - 8x - 12[/tex]

Step 4: Divide both sides by [tex]5x+4[/tex].

[tex]\frac{c(5x +4)}{5x + 4} = \frac{nx-8x-12}{5x + 4}[/tex]

Answer : [tex]\boxed{\frac{nx-8x-12}{5x + 4} }[/tex]

❀Hope this helped you!❀

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Answer:

c = 3 and n = - 7

Step-by-step explanation:

Expand the left side and compare the coefficients of like terms on both sides.

(5x + 4)(2x - c) ← expand using FOIL

= 10x² - 5cx + 8x - 4c ← factor out x from each of the terms in x

= 10x² + x( - 5c + 8) - 4c

Given this is equal to 10x² + nx - 12, then

Comparing the constant terms

- 4c = - 12 ( divide both sides by - 4 )

c = 3

Comparing the coefficients of the x- terms

n = - 5c + 8 = - 5(3) + 8 = - 15 + 8 = - 7

Thus

c = 3 and n = - 7

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