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

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


Simplifying
2x(2x + -5) = 3x(7 + -1x)

Reorder the terms:
2x(-5 + 2x) = 3x(7 + -1x)
(-5 * 2x + 2x * 2x) = 3x(7 + -1x)
(-10x + 4x2) = 3x(7 + -1x)
-10x + 4x2 = (7 * 3x + -1x * 3x)
-10x + 4x2 = (21x + -3x2)

Solving
-10x + 4x2 = 21x + -3x2

Solving for variable 'x'.

Reorder the terms:
-10x + -21x + 4x2 + 3x2 = 21x + -3x2 + -21x + 3x2

Combine like terms: -10x + -21x = -31x
-31x + 4x2 + 3x2 = 21x + -3x2 + -21x + 3x2

Combine like terms: 4x2 + 3x2 = 7x2
-31x + 7x2 = 21x + -3x2 + -21x + 3x2

Reorder the terms:
-31x + 7x2 = 21x + -21x + -3x2 + 3x2

Combine like terms: 21x + -21x = 0
-31x + 7x2 = 0 + -3x2 + 3x2
-31x + 7x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-31x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-31 + 7x) = 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 '(-31 + 7x)' equal to zero and attempt to solve:

Simplifying
-31 + 7x = 0

Solving
-31 + 7x = 0

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

Add '31' to each side of the equation.
-31 + 31 + 7x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 7x = 0 + 31
7x = 0 + 31

Combine like terms: 0 + 31 = 31
7x = 31

Divide each side by '7'.
x = 4.428571429

Simplifying
x = 4.428571429
Solution
x = {0, 4.428571429}

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