2(x^2+x+50)=4x^2-6x+10

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Solution for 2(x^2+x+50)=4x^2-6x+10 equation: 


Simplifying
2(x2 + x + 50) = 4x2 + -6x + 10

Reorder the terms:
2(50 + x + x2) = 4x2 + -6x + 10
(50 * 2 + x * 2 + x2 * 2) = 4x2 + -6x + 10
(100 + 2x + 2x2) = 4x2 + -6x + 10

Reorder the terms:
100 + 2x + 2x2 = 10 + -6x + 4x2

Solving
100 + 2x + 2x2 = 10 + -6x + 4x2

Solving for variable 'x'.

Reorder the terms:
100 + -10 + 2x + 6x + 2x2 + -4x2 = 10 + -6x + 4x2 + -10 + 6x + -4x2

Combine like terms: 100 + -10 = 90
90 + 2x + 6x + 2x2 + -4x2 = 10 + -6x + 4x2 + -10 + 6x + -4x2

Combine like terms: 2x + 6x = 8x
90 + 8x + 2x2 + -4x2 = 10 + -6x + 4x2 + -10 + 6x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
90 + 8x + -2x2 = 10 + -6x + 4x2 + -10 + 6x + -4x2

Reorder the terms:
90 + 8x + -2x2 = 10 + -10 + -6x + 6x + 4x2 + -4x2

Combine like terms: 10 + -10 = 0
90 + 8x + -2x2 = 0 + -6x + 6x + 4x2 + -4x2
90 + 8x + -2x2 = -6x + 6x + 4x2 + -4x2

Combine like terms: -6x + 6x = 0
90 + 8x + -2x2 = 0 + 4x2 + -4x2
90 + 8x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
90 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + 4x + -1x2) = 0

Factor a trinomial.
2((9 + -1x)(5 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9

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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {9, -5}

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