60x^2+3x+5=5x+7

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Solution for 60x^2+3x+5=5x+7 equation: 


Simplifying
60x2 + 3x + 5 = 5x + 7

Reorder the terms:
5 + 3x + 60x2 = 5x + 7

Reorder the terms:
5 + 3x + 60x2 = 7 + 5x

Solving
5 + 3x + 60x2 = 7 + 5x

Solving for variable 'x'.

Reorder the terms:
5 + -7 + 3x + -5x + 60x2 = 7 + 5x + -7 + -5x

Combine like terms: 5 + -7 = -2
-2 + 3x + -5x + 60x2 = 7 + 5x + -7 + -5x

Combine like terms: 3x + -5x = -2x
-2 + -2x + 60x2 = 7 + 5x + -7 + -5x

Reorder the terms:
-2 + -2x + 60x2 = 7 + -7 + 5x + -5x

Combine like terms: 7 + -7 = 0
-2 + -2x + 60x2 = 0 + 5x + -5x
-2 + -2x + 60x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-2 + -2x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1x + 30x2) = 0

Factor a trinomial.
2((-1 + -6x)(1 + -5x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x = 0 + 1
-6x = 0 + 1

Combine like terms: 0 + 1 = 1
-6x = 1

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

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

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

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-0.1666666667, 0.2}

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