# Simplify -(- 4x + 5x^2)+\{-7[-2(-9x^2 + 14x-6)–(8x^2 – 20)] –

Simplify $-\left(-4x+5{x}^{2}\right)+\left\{-7\left[-2\left(-9{x}^{2}+14x-6\right)–\left(8{x}^{2}–20\right)\right]–10x\right\}$
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Marcus Herman
Here we have given
$-\left(-4x+5{x}^{2}\right)+\left\{-7\left[-2\left(-9{x}^{2}+14x-6\right)–\left(8{x}^{2}–20\right)\right]–10x\right\}$
$=\left(4x-5{x}^{2}\right)+\left\{-7\left[18{x}^{2}-28x+12-8{x}^{2}+20\right]-10x\right\}$
$=\left(4x-5{x}^{2}\right)+\left\{-7\left[10{x}^{2}-28x+32\right]-10x\right\}$
$=\left(4x-5{x}^{2}\right)+\left\{-70{x}^{2}+196x+224-10x\right\}$
$=\left(4x-5{x}^{2}\right)+\left(-70{x}^{2}+186x+224\right)=-75{x}^{2}+190x+224$

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William Appel
Simplify the following:
$-\left(5{x}^{2}-4x\right)-7\left(-\left(8{x}^{2}-20\right)-2\left(-9{x}^{2}+14x-6\right)\right)-10x$
Factor out the greatest common divisor of the coefficients of $8{x}^{2}-20.$
Factor 4 out of 8 ${x}^{2}-20:$
$-\left(5{x}^{2}-4x\right)-7\left(-2\left(-9{x}^{2}+14x-6\right)-\left(4\left(2{x}^{2}-5\right)\right)\right)-10x$
Factor common terms out of $5{x}^{2}-4x.$
Factor x out of $5{x}^{2}-4x$:
$-\left(x\left(5x-4\right)\right)-7\left(-2\left(-9{x}^{2}+14x-6\right)-4\left(2{x}^{2}-5\right)\right)-10x$
Distribute -2 over $-9{x}^{2}+14x-6$.
$-2\left(-9{x}^{2}+14x-6\right)=18{x}^{2}-28x+12:$
$-\left(x\left(5x-4\right)\right)-7\left(\left(18{x}^{2}-28x+12\right)-4\left(2{x}^{2}-5\right)\right)-10x$
Distribute -4 over $2{x}^{2}-5.$
$-4\left(2{x}^{2}-5\right)=-8{x}^{2}+20:$
$-\left(x\left(5x-4\right)\right)-7\left(\left(-8{x}^{2}+20\right)+18{x}^{2}-28x+12\right)-10x$
Group like terms in $18{x}^{2}-8{x}^{2}-28x+12+20.$
Grouping like terms, $18{x}^{2}-8{x}^{2}-28x+12+20=\left(18{x}^{2}-8{x}^{2}\right)-28x+\left(12+20\right):$
$-\left(x\left(5x-4\right)\right)-7\left(\left(18{x}^{2}-8{x}^{2}\right)-28x+\left(12+20\right)\right)-10x$
Combine like terms in $18{x}^{2}-8{x}^{2}.$