7(3x-8)=7x(5-3x)

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Solution for 7(3x-8)=7x(5-3x) equation: 


Simplifying
7(3x + -8) = 7x(5 + -3x)

Reorder the terms:
7(-8 + 3x) = 7x(5 + -3x)
(-8 * 7 + 3x * 7) = 7x(5 + -3x)
(-56 + 21x) = 7x(5 + -3x)
-56 + 21x = (5 * 7x + -3x * 7x)
-56 + 21x = (35x + -21x2)

Solving
-56 + 21x = 35x + -21x2

Solving for variable 'x'.

Combine like terms: 21x + -35x = -14x
-56 + -14x + 21x2 = 35x + -21x2 + -35x + 21x2

Reorder the terms:
-56 + -14x + 21x2 = 35x + -35x + -21x2 + 21x2

Combine like terms: 35x + -35x = 0
-56 + -14x + 21x2 = 0 + -21x2 + 21x2
-56 + -14x + 21x2 = -21x2 + 21x2

Combine like terms: -21x2 + 21x2 = 0
-56 + -14x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + -2x + 3x2) = 0

Factor a trinomial.
7((-4 + -3x)(2 + -1x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.333333333, 2}

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