3x^2+2x+8=20x-7

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Solution for 3x^2+2x+8=20x-7 equation: 


Simplifying
3x2 + 2x + 8 = 20x + -7

Reorder the terms:
8 + 2x + 3x2 = 20x + -7

Reorder the terms:
8 + 2x + 3x2 = -7 + 20x

Solving
8 + 2x + 3x2 = -7 + 20x

Solving for variable 'x'.

Reorder the terms:
8 + 7 + 2x + -20x + 3x2 = -7 + 20x + 7 + -20x

Combine like terms: 8 + 7 = 15
15 + 2x + -20x + 3x2 = -7 + 20x + 7 + -20x

Combine like terms: 2x + -20x = -18x
15 + -18x + 3x2 = -7 + 20x + 7 + -20x

Reorder the terms:
15 + -18x + 3x2 = -7 + 7 + 20x + -20x

Combine like terms: -7 + 7 = 0
15 + -18x + 3x2 = 0 + 20x + -20x
15 + -18x + 3x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
15 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -6x + x2) = 0

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

Ignore the factor 3.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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