4x^2-10+8x+5+x^2+2x+10=180

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Solution for 4x^2-10+8x+5+x^2+2x+10=180 equation: 


Simplifying
4x2 + -10 + 8x + 5 + x2 + 2x + 10 = 180

Reorder the terms:
-10 + 5 + 10 + 8x + 2x + 4x2 + x2 = 180

Combine like terms: -10 + 5 = -5
-5 + 10 + 8x + 2x + 4x2 + x2 = 180

Combine like terms: -5 + 10 = 5
5 + 8x + 2x + 4x2 + x2 = 180

Combine like terms: 8x + 2x = 10x
5 + 10x + 4x2 + x2 = 180

Combine like terms: 4x2 + x2 = 5x2
5 + 10x + 5x2 = 180

Solving
5 + 10x + 5x2 = 180

Solving for variable 'x'.

Reorder the terms:
5 + -180 + 10x + 5x2 = 180 + -180

Combine like terms: 5 + -180 = -175
-175 + 10x + 5x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-175 + 10x + 5x2 = 0

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

Factor a trinomial.
5((-7 + -1x)(5 + -1x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-7, 5}

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