3x(x-5)=7x(x)-16x

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Solution for 3x(x-5)=7x(x)-16x equation: 


Simplifying
3x(x + -5) = 7x(x) + -16x

Reorder the terms:
3x(-5 + x) = 7x(x) + -16x
(-5 * 3x + x * 3x) = 7x(x) + -16x
(-15x + 3x2) = 7x(x) + -16x

Multiply x * x
-15x + 3x2 = 7x2 + -16x

Reorder the terms:
-15x + 3x2 = -16x + 7x2

Solving
-15x + 3x2 = -16x + 7x2

Solving for variable 'x'.

Reorder the terms:
-15x + 16x + 3x2 + -7x2 = -16x + 7x2 + 16x + -7x2

Combine like terms: -15x + 16x = 1x
1x + 3x2 + -7x2 = -16x + 7x2 + 16x + -7x2

Combine like terms: 3x2 + -7x2 = -4x2
1x + -4x2 = -16x + 7x2 + 16x + -7x2

Reorder the terms:
1x + -4x2 = -16x + 16x + 7x2 + -7x2

Combine like terms: -16x + 16x = 0
1x + -4x2 = 0 + 7x2 + -7x2
1x + -4x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
1x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -4x) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, 0.25}

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