0=5x^2-10x-175

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Solution for 0=5x^2-10x-175 equation: 


Simplifying
0 = 5x2 + -10x + -175

Reorder the terms:
0 = -175 + -10x + 5x2

Solving
0 = -175 + -10x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 175 = 175
175 + 10x + -5x2 = -175 + -10x + 5x2 + 175 + 10x + -5x2

Reorder the terms:
175 + 10x + -5x2 = -175 + 175 + -10x + 10x + 5x2 + -5x2

Combine like terms: -175 + 175 = 0
175 + 10x + -5x2 = 0 + -10x + 10x + 5x2 + -5x2
175 + 10x + -5x2 = -10x + 10x + 5x2 + -5x2

Combine like terms: -10x + 10x = 0
175 + 10x + -5x2 = 0 + 5x2 + -5x2
175 + 10x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
175 + 10x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(35 + 2x + -1x2) = 0

Factor a trinomial.
5((7 + -1x)(5 + x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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 = {7, -5}

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