5x^2-20x-10=5x-40

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Solution for 5x^2-20x-10=5x-40 equation: 


Simplifying
5x2 + -20x + -10 = 5x + -40

Reorder the terms:
-10 + -20x + 5x2 = 5x + -40

Reorder the terms:
-10 + -20x + 5x2 = -40 + 5x

Solving
-10 + -20x + 5x2 = -40 + 5x

Solving for variable 'x'.

Reorder the terms:
-10 + 40 + -20x + -5x + 5x2 = -40 + 5x + 40 + -5x

Combine like terms: -10 + 40 = 30
30 + -20x + -5x + 5x2 = -40 + 5x + 40 + -5x

Combine like terms: -20x + -5x = -25x
30 + -25x + 5x2 = -40 + 5x + 40 + -5x

Reorder the terms:
30 + -25x + 5x2 = -40 + 40 + 5x + -5x

Combine like terms: -40 + 40 = 0
30 + -25x + 5x2 = 0 + 5x + -5x
30 + -25x + 5x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
30 + -25x + 5x2 = 0

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

Factor a trinomial.
5((2 + -1x)(3 + -1x)) = 0

Ignore the factor 5.

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}

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