# How do you solve for x in this problem? 4x^2−3=−x?

How do you solve for x in this problem? $4{x}^{2}-3=-x$?
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$\text{rearrange into standard form}\phantom{\rule{1ex}{0ex}}xa{x}^{2}+bx+c=0$
$⇒4{x}^{2}+x-3=0←\text{in standard form}$
factor the quadratic using the a-c method
$\text{the factors of the product}\phantom{\rule{1ex}{0ex}}4×-3=-12$
which sum to + 1 are + 4 and - 3
split the middle term using these factors
$4{x}^{2}+4x-3x-3=0←\text{factor by grouping}$
4x(x+1)−3(x+1)=0
take out the common factor (x+1)
$⇒\left(x+1\right)\left(4x-3\right)=0$
equate each factor to zero and solve for x
$x+1=0⇒x=-1$
$4x-3=0⇒x=\frac{3}{4}$