5x^2+5x=20x-10

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Solution for 5x^2+5x=20x-10 equation: 


Simplifying
5x2 + 5x = 20x + -10

Reorder the terms:
5x + 5x2 = 20x + -10

Reorder the terms:
5x + 5x2 = -10 + 20x

Solving
5x + 5x2 = -10 + 20x

Solving for variable 'x'.

Reorder the terms:
10 + 5x + -20x + 5x2 = -10 + 20x + 10 + -20x

Combine like terms: 5x + -20x = -15x
10 + -15x + 5x2 = -10 + 20x + 10 + -20x

Reorder the terms:
10 + -15x + 5x2 = -10 + 10 + 20x + -20x

Combine like terms: -10 + 10 = 0
10 + -15x + 5x2 = 0 + 20x + -20x
10 + -15x + 5x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
10 + -15x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -3x + x2) = 0

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

Ignore the factor 5.

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 '(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
Solution
x = {1, 2}

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