30x^3-42x^2=-20x^3+28x^2

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Solution for 30x^3-42x^2=-20x^3+28x^2 equation: 


Simplifying
30x3 + -42x2 = -20x3 + 28x2

Reorder the terms:
-42x2 + 30x3 = -20x3 + 28x2

Reorder the terms:
-42x2 + 30x3 = 28x2 + -20x3

Solving
-42x2 + 30x3 = 28x2 + -20x3

Solving for variable 'x'.

Reorder the terms:
-42x2 + -28x2 + 30x3 + 20x3 = 28x2 + -20x3 + -28x2 + 20x3

Combine like terms: -42x2 + -28x2 = -70x2
-70x2 + 30x3 + 20x3 = 28x2 + -20x3 + -28x2 + 20x3

Combine like terms: 30x3 + 20x3 = 50x3
-70x2 + 50x3 = 28x2 + -20x3 + -28x2 + 20x3

Reorder the terms:
-70x2 + 50x3 = 28x2 + -28x2 + -20x3 + 20x3

Combine like terms: 28x2 + -28x2 = 0
-70x2 + 50x3 = 0 + -20x3 + 20x3
-70x2 + 50x3 = -20x3 + 20x3

Combine like terms: -20x3 + 20x3 = 0
-70x2 + 50x3 = 0

Factor out the Greatest Common Factor (GCF), '10x2'.
10x2(-7 + 5x) = 0

Ignore the factor 10.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-7 + 5x)' equal to zero and attempt to solve:

Simplifying
-7 + 5x = 0

Solving
-7 + 5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + 5x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 5x = 0 + 7
5x = 0 + 7

Combine like terms: 0 + 7 = 7
5x = 7

Divide each side by '5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {0, 1.4}

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