4x^2-37x=5x-20

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Solution for 4x^2-37x=5x-20 equation: 


Simplifying
4x2 + -37x = 5x + -20

Reorder the terms:
-37x + 4x2 = 5x + -20

Reorder the terms:
-37x + 4x2 = -20 + 5x

Solving
-37x + 4x2 = -20 + 5x

Solving for variable 'x'.

Reorder the terms:
20 + -37x + -5x + 4x2 = -20 + 5x + 20 + -5x

Combine like terms: -37x + -5x = -42x
20 + -42x + 4x2 = -20 + 5x + 20 + -5x

Reorder the terms:
20 + -42x + 4x2 = -20 + 20 + 5x + -5x

Combine like terms: -20 + 20 = 0
20 + -42x + 4x2 = 0 + 5x + -5x
20 + -42x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
20 + -42x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -21x + 2x2) = 0

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

Ignore the factor 2.

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

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0.5, 10}

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