35x^2-60x=101x+70

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Solution for 35x^2-60x=101x+70 equation: 


Simplifying
35x2 + -60x = 101x + 70

Reorder the terms:
-60x + 35x2 = 101x + 70

Reorder the terms:
-60x + 35x2 = 70 + 101x

Solving
-60x + 35x2 = 70 + 101x

Solving for variable 'x'.

Reorder the terms:
-70 + -60x + -101x + 35x2 = 70 + 101x + -70 + -101x

Combine like terms: -60x + -101x = -161x
-70 + -161x + 35x2 = 70 + 101x + -70 + -101x

Reorder the terms:
-70 + -161x + 35x2 = 70 + -70 + 101x + -101x

Combine like terms: 70 + -70 = 0
-70 + -161x + 35x2 = 0 + 101x + -101x
-70 + -161x + 35x2 = 101x + -101x

Combine like terms: 101x + -101x = 0
-70 + -161x + 35x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-10 + -23x + 5x2) = 0

Factor a trinomial.
7((-2 + -5x)(5 + -1x)) = 0

Ignore the factor 7.

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

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

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

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

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

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 = {-0.4, 5}

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