20x^2-15=5x^2+31x-3

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Solution for 20x^2-15=5x^2+31x-3 equation: 


Simplifying
20x2 + -15 = 5x2 + 31x + -3

Reorder the terms:
-15 + 20x2 = 5x2 + 31x + -3

Reorder the terms:
-15 + 20x2 = -3 + 31x + 5x2

Solving
-15 + 20x2 = -3 + 31x + 5x2

Solving for variable 'x'.

Reorder the terms:
-15 + 3 + -31x + 20x2 + -5x2 = -3 + 31x + 5x2 + 3 + -31x + -5x2

Combine like terms: -15 + 3 = -12
-12 + -31x + 20x2 + -5x2 = -3 + 31x + 5x2 + 3 + -31x + -5x2

Combine like terms: 20x2 + -5x2 = 15x2
-12 + -31x + 15x2 = -3 + 31x + 5x2 + 3 + -31x + -5x2

Reorder the terms:
-12 + -31x + 15x2 = -3 + 3 + 31x + -31x + 5x2 + -5x2

Combine like terms: -3 + 3 = 0
-12 + -31x + 15x2 = 0 + 31x + -31x + 5x2 + -5x2
-12 + -31x + 15x2 = 31x + -31x + 5x2 + -5x2

Combine like terms: 31x + -31x = 0
-12 + -31x + 15x2 = 0 + 5x2 + -5x2
-12 + -31x + 15x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-12 + -31x + 15x2 = 0

Factor a trinomial.
(-1 + -3x)(12 + -5x) = 0


Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(12 + -5x)' equal to zero and attempt to solve:

Simplifying
12 + -5x = 0

Solving
12 + -5x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -5x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5x = 0 + -12
-5x = 0 + -12

Combine like terms: 0 + -12 = -12
-5x = -12

Divide each side by '-5'.
x = 2.4

Simplifying
x = 2.4
Solution
x = {-0.3333333333, 2.4}

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