4x(x-5)=19x^2-21x

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Solution for 4x(x-5)=19x^2-21x equation: 


Simplifying
4x(x + -5) = 19x2 + -21x

Reorder the terms:
4x(-5 + x) = 19x2 + -21x
(-5 * 4x + x * 4x) = 19x2 + -21x
(-20x + 4x2) = 19x2 + -21x

Reorder the terms:
-20x + 4x2 = -21x + 19x2

Solving
-20x + 4x2 = -21x + 19x2

Solving for variable 'x'.

Reorder the terms:
-20x + 21x + 4x2 + -19x2 = -21x + 19x2 + 21x + -19x2

Combine like terms: -20x + 21x = 1x
1x + 4x2 + -19x2 = -21x + 19x2 + 21x + -19x2

Combine like terms: 4x2 + -19x2 = -15x2
1x + -15x2 = -21x + 19x2 + 21x + -19x2

Reorder the terms:
1x + -15x2 = -21x + 21x + 19x2 + -19x2

Combine like terms: -21x + 21x = 0
1x + -15x2 = 0 + 19x2 + -19x2
1x + -15x2 = 19x2 + -19x2

Combine like terms: 19x2 + -19x2 = 0
1x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -15x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + -15x)' equal to zero and attempt to solve:

Simplifying
1 + -15x = 0

Solving
1 + -15x = 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 + -15x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -15x = 0 + -1
-15x = 0 + -1

Combine like terms: 0 + -1 = -1
-15x = -1

Divide each side by '-15'.
x = 0.06666666667

Simplifying
x = 0.06666666667
Solution
x = {0, 0.06666666667}

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