Question
Simplify the expression
45x3+246x2+168x
Evaluate
(−5x−4)(−9x2−6x×7)
Multiply the terms
(−5x−4)(−9x2−42x)
Apply the distributive property
−5x(−9x2)−(−5x×42x)−4(−9x2)−(−4×42x)
Multiply the terms
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Evaluate
−5x(−9x2)
Multiply the numbers
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Evaluate
−5(−9)
Multiplying or dividing an even number of negative terms equals a positive
5×9
Multiply the numbers
45
45x×x2
Multiply the terms
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
45x3
45x3−(−5x×42x)−4(−9x2)−(−4×42x)
Multiply the terms
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Evaluate
−5x×42x
Multiply the numbers
−210x×x
Multiply the terms
−210x2
45x3−(−210x2)−4(−9x2)−(−4×42x)
Multiply the numbers
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Evaluate
−4(−9)
Multiplying or dividing an even number of negative terms equals a positive
4×9
Multiply the numbers
36
45x3−(−210x2)+36x2−(−4×42x)
Multiply the numbers
45x3−(−210x2)+36x2−(−168x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
45x3+210x2+36x2+168x
Solution
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Evaluate
210x2+36x2
Collect like terms by calculating the sum or difference of their coefficients
(210+36)x2
Add the numbers
246x2
45x3+246x2+168x
Show Solution

Factor the expression
3x(5x+4)(3x+14)
Evaluate
(−5x−4)(−9x2−6x×7)
Multiply the terms
(−5x−4)(−9x2−42x)
Factor the expression
−(5x+4)(−9x2−42x)
Factor the expression
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Evaluate
−9x2−42x
Rewrite the expression
−3x×3x−3x×14
Factor out −3x from the expression
−3x(3x+14)
−(5x+4)(−3x)(3x+14)
Solution
3x(5x+4)(3x+14)
Show Solution

Find the roots
x1=−314,x2=−54,x3=0
Alternative Form
x1=−4.6˙,x2=−0.8,x3=0
Evaluate
(−5x−4)(−9x2−6x×7)
To find the roots of the expression,set the expression equal to 0
(−5x−4)(−9x2−6x×7)=0
Multiply the terms
(−5x−4)(−9x2−42x)=0
Change the sign
(5x+4)(−9x2−42x)=0
Separate the equation into 2 possible cases
5x+4=0−9x2−42x=0
Solve the equation
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Evaluate
5x+4=0
Move the constant to the right-hand side and change its sign
5x=0−4
Removing 0 doesn't change the value,so remove it from the expression
5x=−4
Divide both sides
55x=5−4
Divide the numbers
x=5−4
Use b−a=−ba=−ba to rewrite the fraction
x=−54
x=−54−9x2−42x=0
Solve the equation
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Evaluate
−9x2−42x=0
Factor the expression
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Evaluate
−9x2−42x
Rewrite the expression
−3x×3x−3x×14
Factor out −3x from the expression
−3x(3x+14)
−3x(3x+14)=0
When the product of factors equals 0,at least one factor is 0
−3x=03x+14=0
Solve the equation for x
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Evaluate
−3x=0
Change the signs on both sides of the equation
3x=0
Rewrite the expression
x=0
x=03x+14=0
Solve the equation for x
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Evaluate
3x+14=0
Move the constant to the right-hand side and change its sign
3x=0−14
Removing 0 doesn't change the value,so remove it from the expression
3x=−14
Divide both sides
33x=3−14
Divide the numbers
x=3−14
Use b−a=−ba=−ba to rewrite the fraction
x=−314
x=0x=−314
x=−54x=0x=−314
Solution
x1=−314,x2=−54,x3=0
Alternative Form
x1=−4.6˙,x2=−0.8,x3=0
Show Solution
