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

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


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

Reorder the terms:
7x(2 + 3x) = 5x(5x + -2)
(2 * 7x + 3x * 7x) = 5x(5x + -2)
(14x + 21x2) = 5x(5x + -2)

Reorder the terms:
14x + 21x2 = 5x(-2 + 5x)
14x + 21x2 = (-2 * 5x + 5x * 5x)
14x + 21x2 = (-10x + 25x2)

Solving
14x + 21x2 = -10x + 25x2

Solving for variable 'x'.

Reorder the terms:
14x + 10x + 21x2 + -25x2 = -10x + 25x2 + 10x + -25x2

Combine like terms: 14x + 10x = 24x
24x + 21x2 + -25x2 = -10x + 25x2 + 10x + -25x2

Combine like terms: 21x2 + -25x2 = -4x2
24x + -4x2 = -10x + 25x2 + 10x + -25x2

Reorder the terms:
24x + -4x2 = -10x + 10x + 25x2 + -25x2

Combine like terms: -10x + 10x = 0
24x + -4x2 = 0 + 25x2 + -25x2
24x + -4x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(6 + -1x) = 0

Ignore the factor 4.

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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 6}

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