3x(x+7)=x(7x-4)

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Solution for 3x(x+7)=x(7x-4) equation: 


Simplifying
3x(x + 7) = x(7x + -4)

Reorder the terms:
3x(7 + x) = x(7x + -4)
(7 * 3x + x * 3x) = x(7x + -4)
(21x + 3x2) = x(7x + -4)

Reorder the terms:
21x + 3x2 = x(-4 + 7x)
21x + 3x2 = (-4 * x + 7x * x)
21x + 3x2 = (-4x + 7x2)

Solving
21x + 3x2 = -4x + 7x2

Solving for variable 'x'.

Reorder the terms:
21x + 4x + 3x2 + -7x2 = -4x + 7x2 + 4x + -7x2

Combine like terms: 21x + 4x = 25x
25x + 3x2 + -7x2 = -4x + 7x2 + 4x + -7x2

Combine like terms: 3x2 + -7x2 = -4x2
25x + -4x2 = -4x + 7x2 + 4x + -7x2

Reorder the terms:
25x + -4x2 = -4x + 4x + 7x2 + -7x2

Combine like terms: -4x + 4x = 0
25x + -4x2 = 0 + 7x2 + -7x2
25x + -4x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
25x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(25 + -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 '(25 + -4x)' equal to zero and attempt to solve:

Simplifying
25 + -4x = 0

Solving
25 + -4x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -4x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -4x = 0 + -25
-4x = 0 + -25

Combine like terms: 0 + -25 = -25
-4x = -25

Divide each side by '-4'.
x = 6.25

Simplifying
x = 6.25
Solution
x = {0, 6.25}

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