48x^2-69x+20=7x^2-8

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Solution for 48x^2-69x+20=7x^2-8 equation: 


Simplifying
48x2 + -69x + 20 = 7x2 + -8

Reorder the terms:
20 + -69x + 48x2 = 7x2 + -8

Reorder the terms:
20 + -69x + 48x2 = -8 + 7x2

Solving
20 + -69x + 48x2 = -8 + 7x2

Solving for variable 'x'.

Reorder the terms:
20 + 8 + -69x + 48x2 + -7x2 = -8 + 7x2 + 8 + -7x2

Combine like terms: 20 + 8 = 28
28 + -69x + 48x2 + -7x2 = -8 + 7x2 + 8 + -7x2

Combine like terms: 48x2 + -7x2 = 41x2
28 + -69x + 41x2 = -8 + 7x2 + 8 + -7x2

Reorder the terms:
28 + -69x + 41x2 = -8 + 8 + 7x2 + -7x2

Combine like terms: -8 + 8 = 0
28 + -69x + 41x2 = 0 + 7x2 + -7x2
28 + -69x + 41x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
28 + -69x + 41x2 = 0

Factor a trinomial.
(28 + -41x)(1 + -1x) = 0


Subproblem 1
Set the factor '(28 + -41x)' equal to zero and attempt to solve:

Simplifying
28 + -41x = 0

Solving
28 + -41x = 0

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

Add '-28' to each side of the equation.
28 + -28 + -41x = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -41x = 0 + -28
-41x = 0 + -28

Combine like terms: 0 + -28 = -28
-41x = -28

Divide each side by '-41'.
x = 0.6829268293

Simplifying
x = 0.6829268293

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0.6829268293, 1}

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