10x^2-3x-20=28+x

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Solution for 10x^2-3x-20=28+x equation: 


Simplifying
10x2 + -3x + -20 = 28 + x

Reorder the terms:
-20 + -3x + 10x2 = 28 + x

Solving
-20 + -3x + 10x2 = 28 + x

Solving for variable 'x'.

Reorder the terms:
-20 + -28 + -3x + -1x + 10x2 = 28 + x + -28 + -1x

Combine like terms: -20 + -28 = -48
-48 + -3x + -1x + 10x2 = 28 + x + -28 + -1x

Combine like terms: -3x + -1x = -4x
-48 + -4x + 10x2 = 28 + x + -28 + -1x

Reorder the terms:
-48 + -4x + 10x2 = 28 + -28 + x + -1x

Combine like terms: 28 + -28 = 0
-48 + -4x + 10x2 = 0 + x + -1x
-48 + -4x + 10x2 = x + -1x

Combine like terms: x + -1x = 0
-48 + -4x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -2x + 5x2) = 0

Factor a trinomial.
2((-2 + -1x)(12 + -5x)) = 0

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 2.4}

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