3x^2+8x=15x-3x^2+20

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Solution for 3x^2+8x=15x-3x^2+20 equation: 


Simplifying
3x2 + 8x = 15x + -3x2 + 20

Reorder the terms:
8x + 3x2 = 15x + -3x2 + 20

Reorder the terms:
8x + 3x2 = 20 + 15x + -3x2

Solving
8x + 3x2 = 20 + 15x + -3x2

Solving for variable 'x'.

Reorder the terms:
-20 + 8x + -15x + 3x2 + 3x2 = 20 + 15x + -3x2 + -20 + -15x + 3x2

Combine like terms: 8x + -15x = -7x
-20 + -7x + 3x2 + 3x2 = 20 + 15x + -3x2 + -20 + -15x + 3x2

Combine like terms: 3x2 + 3x2 = 6x2
-20 + -7x + 6x2 = 20 + 15x + -3x2 + -20 + -15x + 3x2

Reorder the terms:
-20 + -7x + 6x2 = 20 + -20 + 15x + -15x + -3x2 + 3x2

Combine like terms: 20 + -20 = 0
-20 + -7x + 6x2 = 0 + 15x + -15x + -3x2 + 3x2
-20 + -7x + 6x2 = 15x + -15x + -3x2 + 3x2

Combine like terms: 15x + -15x = 0
-20 + -7x + 6x2 = 0 + -3x2 + 3x2
-20 + -7x + 6x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-20 + -7x + 6x2 = 0

Factor a trinomial.
(-4 + -3x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-1.333333333, 2.5}

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