Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1≈0.117928,x2≈3.882072
Evaluate
∣3x−6∣∣x−2∣∣2−x∣=20
Multiply the terms
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Evaluate
∣3x−6∣∣x−2∣∣2−x∣
Multiply the first two terms
∣(3x−6)(x−2)∣∣2−x∣
Multiply the terms
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Evaluate
(3x−6)(x−2)(2−x)
Multiply the terms
(3x−6)(−(x−2)2)
Use the commutative property to reorder the terms
(−3x+6)(x−2)2
(−3x+6)(x−2)2
(−3x+6)(x−2)2=20
Separate the equation into 2 possible cases
(−3x+6)(x−2)2=20(−3x+6)(x−2)2=−20
Solve the equation for x
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Evaluate
(−3x+6)(x−2)2=20
Change the sign
(3x−6)(x−2)2=−20
Expand the expression
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Evaluate
(3x−6)(x−2)2
Expand the expression
(3x−6)(x2−4x+4)
Apply the distributive property
3x×x2−3x×4x+3x×4−6x2−(−6×4x)−6×4
Multiply the terms
3x3−3x×4x+3x×4−6x2−(−6×4x)−6×4
Multiply the terms
3x3−12x2+3x×4−6x2−(−6×4x)−6×4
Multiply the numbers
3x3−12x2+12x−6x2−(−6×4x)−6×4
Multiply the numbers
3x3−12x2+12x−6x2−(−24x)−6×4
Multiply the numbers
3x3−12x2+12x−6x2−(−24x)−24
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
3x3−12x2+12x−6x2+24x−24
Subtract the terms
3x3−18x2+12x+24x−24
Add the terms
3x3−18x2+36x−24
3x3−18x2+36x−24=−20
Move the expression to the left side
3x3−18x2+36x−24−(−20)=0
Subtract the numbers
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Evaluate
−24−(−20)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−24+20
Add the numbers
−4
3x3−18x2+36x−4=0
Calculate
x≈0.117928
x≈0.117928(−3x+6)(x−2)2=−20
Solve the equation for x
More Steps
Evaluate
(−3x+6)(x−2)2=−20
Change the sign
(3x−6)(x−2)2=20
Expand the expression
More Steps
Evaluate
(3x−6)(x−2)2
Expand the expression
(3x−6)(x2−4x+4)
Apply the distributive property
3x×x2−3x×4x+3x×4−6x2−(−6×4x)−6×4
Multiply the terms
3x3−3x×4x+3x×4−6x2−(−6×4x)−6×4
Multiply the terms
3x3−12x2+3x×4−6x2−(−6×4x)−6×4
Multiply the numbers
3x3−12x2+12x−6x2−(−6×4x)−6×4
Multiply the numbers
3x3−12x2+12x−6x2−(−24x)−6×4
Multiply the numbers
3x3−12x2+12x−6x2−(−24x)−24
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
3x3−12x2+12x−6x2+24x−24
Subtract the terms
3x3−18x2+12x+24x−24
Add the terms
3x3−18x2+36x−24
3x3−18x2+36x−24=20
Move the expression to the left side
3x3−18x2+36x−24−20=0
Subtract the numbers
3x3−18x2+36x−44=0
Calculate
x≈3.882072
x≈0.117928x≈3.882072
Solution
x1≈0.117928,x2≈3.882072
Show Solution
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