42y^2-69y+20=7y^2-8

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Solution for 42y^2-69y+20=7y^2-8 equation: 


Simplifying
42y2 + -69y + 20 = 7y2 + -8

Reorder the terms:
20 + -69y + 42y2 = 7y2 + -8

Reorder the terms:
20 + -69y + 42y2 = -8 + 7y2

Solving
20 + -69y + 42y2 = -8 + 7y2

Solving for variable 'y'.

Reorder the terms:
20 + 8 + -69y + 42y2 + -7y2 = -8 + 7y2 + 8 + -7y2

Combine like terms: 20 + 8 = 28
28 + -69y + 42y2 + -7y2 = -8 + 7y2 + 8 + -7y2

Combine like terms: 42y2 + -7y2 = 35y2
28 + -69y + 35y2 = -8 + 7y2 + 8 + -7y2

Reorder the terms:
28 + -69y + 35y2 = -8 + 8 + 7y2 + -7y2

Combine like terms: -8 + 8 = 0
28 + -69y + 35y2 = 0 + 7y2 + -7y2
28 + -69y + 35y2 = 7y2 + -7y2

Combine like terms: 7y2 + -7y2 = 0
28 + -69y + 35y2 = 0

Factor a trinomial.
(4 + -7y)(7 + -5y) = 0


Subproblem 1
Set the factor '(4 + -7y)' equal to zero and attempt to solve:

Simplifying
4 + -7y = 0

Solving
4 + -7y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7y = 0 + -4
-7y = 0 + -4

Combine like terms: 0 + -4 = -4
-7y = -4

Divide each side by '-7'.
y = 0.5714285714

Simplifying
y = 0.5714285714

Subproblem 2
Set the factor '(7 + -5y)' equal to zero and attempt to solve:

Simplifying
7 + -5y = 0

Solving
7 + -5y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5y = 0 + -7
-5y = 0 + -7

Combine like terms: 0 + -7 = -7
-5y = -7

Divide each side by '-5'.
y = 1.4

Simplifying
y = 1.4
Solution
y = {0.5714285714, 1.4}

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