3x(x-5)=7x(2)-16x

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Solution for 3x(x-5)=7x(2)-16x equation: 


Simplifying
3x(x + -5) = 7x(2) + -16x

Reorder the terms:
3x(-5 + x) = 7x(2) + -16x
(-5 * 3x + x * 3x) = 7x(2) + -16x
(-15x + 3x2) = 7x(2) + -16x

Reorder the terms for easier multiplication:
-15x + 3x2 = 7 * 2x + -16x

Multiply 7 * 2
-15x + 3x2 = 14x + -16x

Combine like terms: 14x + -16x = -2x
-15x + 3x2 = -2x

Solving
-15x + 3x2 = -2x

Solving for variable 'x'.

Reorder the terms:
-15x + 2x + 3x2 = -2x + 2x

Combine like terms: -15x + 2x = -13x
-13x + 3x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-13x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-13 + 3x) = 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 '(-13 + 3x)' equal to zero and attempt to solve:

Simplifying
-13 + 3x = 0

Solving
-13 + 3x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 3x = 0 + 13
3x = 0 + 13

Combine like terms: 0 + 13 = 13
3x = 13

Divide each side by '3'.
x = 4.333333333

Simplifying
x = 4.333333333
Solution
x = {0, 4.333333333}

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