Question
Simplify the expression
6x4−5x−24x3+20
Evaluate
(x−4)(2x2×3x−5)
Multiply
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Evaluate
2x2×3x
Multiply the terms
6x2×x
Multiply the terms with the same base by adding their exponents
6x2+1
Add the numbers
6x3
(x−4)(6x3−5)
Apply the distributive property
x×6x3−x×5−4×6x3−(−4×5)
Multiply the terms
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Evaluate
x×6x3
Use the commutative property to reorder the terms
6x×x3
Multiply the terms
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Evaluate
x×x3
Use the product rule an×am=an+m to simplify the expression
x1+3
Add the numbers
x4
6x4
6x4−x×5−4×6x3−(−4×5)
Use the commutative property to reorder the terms
6x4−5x−4×6x3−(−4×5)
Multiply the numbers
6x4−5x−24x3−(−4×5)
Multiply the numbers
6x4−5x−24x3−(−20)
Solution
6x4−5x−24x3+20
Show Solution

Find the roots
x1=63180,x2=4
Alternative Form
x1≈0.941036,x2=4
Evaluate
(x−4)(2x2×3x−5)
To find the roots of the expression,set the expression equal to 0
(x−4)(2x2×3x−5)=0
Multiply
More Steps

Multiply the terms
2x2×3x
Multiply the terms
6x2×x
Multiply the terms with the same base by adding their exponents
6x2+1
Add the numbers
6x3
(x−4)(6x3−5)=0
Separate the equation into 2 possible cases
x−4=06x3−5=0
Solve the equation
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Evaluate
x−4=0
Move the constant to the right-hand side and change its sign
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
x=46x3−5=0
Solve the equation
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Evaluate
6x3−5=0
Move the constant to the right-hand side and change its sign
6x3=0+5
Removing 0 doesn't change the value,so remove it from the expression
6x3=5
Divide both sides
66x3=65
Divide the numbers
x3=65
Take the 3-th root on both sides of the equation
3x3=365
Calculate
x=365
Simplify the root
More Steps

Evaluate
365
To take a root of a fraction,take the root of the numerator and denominator separately
3635
Multiply by the Conjugate
36×36235×362
Simplify
36×36235×336
Multiply the numbers
36×3623180
Multiply the numbers
63180
x=63180
x=4x=63180
Solution
x1=63180,x2=4
Alternative Form
x1≈0.941036,x2=4
Show Solution
