30x^2-80x+50=7x-4

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Solution for 30x^2-80x+50=7x-4 equation: 


Simplifying
30x2 + -80x + 50 = 7x + -4

Reorder the terms:
50 + -80x + 30x2 = 7x + -4

Reorder the terms:
50 + -80x + 30x2 = -4 + 7x

Solving
50 + -80x + 30x2 = -4 + 7x

Solving for variable 'x'.

Reorder the terms:
50 + 4 + -80x + -7x + 30x2 = -4 + 7x + 4 + -7x

Combine like terms: 50 + 4 = 54
54 + -80x + -7x + 30x2 = -4 + 7x + 4 + -7x

Combine like terms: -80x + -7x = -87x
54 + -87x + 30x2 = -4 + 7x + 4 + -7x

Reorder the terms:
54 + -87x + 30x2 = -4 + 4 + 7x + -7x

Combine like terms: -4 + 4 = 0
54 + -87x + 30x2 = 0 + 7x + -7x
54 + -87x + 30x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
54 + -87x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -29x + 10x2) = 0

Factor a trinomial.
3((9 + -10x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + -10x)' equal to zero and attempt to solve:

Simplifying
9 + -10x = 0

Solving
9 + -10x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -10x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -10x = 0 + -9
-10x = 0 + -9

Combine like terms: 0 + -9 = -9
-10x = -9

Divide each side by '-10'.
x = 0.9

Simplifying
x = 0.9

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.9, 2}

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