75x^2-75x-67=5x+8

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Solution for 75x^2-75x-67=5x+8 equation: 


Simplifying
75x2 + -75x + -67 = 5x + 8

Reorder the terms:
-67 + -75x + 75x2 = 5x + 8

Reorder the terms:
-67 + -75x + 75x2 = 8 + 5x

Solving
-67 + -75x + 75x2 = 8 + 5x

Solving for variable 'x'.

Reorder the terms:
-67 + -8 + -75x + -5x + 75x2 = 8 + 5x + -8 + -5x

Combine like terms: -67 + -8 = -75
-75 + -75x + -5x + 75x2 = 8 + 5x + -8 + -5x

Combine like terms: -75x + -5x = -80x
-75 + -80x + 75x2 = 8 + 5x + -8 + -5x

Reorder the terms:
-75 + -80x + 75x2 = 8 + -8 + 5x + -5x

Combine like terms: 8 + -8 = 0
-75 + -80x + 75x2 = 0 + 5x + -5x
-75 + -80x + 75x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-75 + -80x + 75x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + -16x + 15x2) = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-0.6, 1.666666667}

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