25x^2-171x+152=x-8-3x^2

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Solution for 25x^2-171x+152=x-8-3x^2 equation: 


Simplifying
25x2 + -171x + 152 = x + -8 + -3x2

Reorder the terms:
152 + -171x + 25x2 = x + -8 + -3x2

Reorder the terms:
152 + -171x + 25x2 = -8 + x + -3x2

Solving
152 + -171x + 25x2 = -8 + x + -3x2

Solving for variable 'x'.

Reorder the terms:
152 + 8 + -171x + -1x + 25x2 + 3x2 = -8 + x + -3x2 + 8 + -1x + 3x2

Combine like terms: 152 + 8 = 160
160 + -171x + -1x + 25x2 + 3x2 = -8 + x + -3x2 + 8 + -1x + 3x2

Combine like terms: -171x + -1x = -172x
160 + -172x + 25x2 + 3x2 = -8 + x + -3x2 + 8 + -1x + 3x2

Combine like terms: 25x2 + 3x2 = 28x2
160 + -172x + 28x2 = -8 + x + -3x2 + 8 + -1x + 3x2

Reorder the terms:
160 + -172x + 28x2 = -8 + 8 + x + -1x + -3x2 + 3x2

Combine like terms: -8 + 8 = 0
160 + -172x + 28x2 = 0 + x + -1x + -3x2 + 3x2
160 + -172x + 28x2 = x + -1x + -3x2 + 3x2

Combine like terms: x + -1x = 0
160 + -172x + 28x2 = 0 + -3x2 + 3x2
160 + -172x + 28x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
160 + -172x + 28x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + -43x + 7x2) = 0

Factor a trinomial.
4((8 + -7x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143

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 = {1.142857143, 5}

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