3x(x-8)=4x(3x+7)

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Solution for 3x(x-8)=4x(3x+7) equation: 


Simplifying
3x(x + -8) = 4x(3x + 7)

Reorder the terms:
3x(-8 + x) = 4x(3x + 7)
(-8 * 3x + x * 3x) = 4x(3x + 7)
(-24x + 3x2) = 4x(3x + 7)

Reorder the terms:
-24x + 3x2 = 4x(7 + 3x)
-24x + 3x2 = (7 * 4x + 3x * 4x)
-24x + 3x2 = (28x + 12x2)

Solving
-24x + 3x2 = 28x + 12x2

Solving for variable 'x'.

Reorder the terms:
-24x + -28x + 3x2 + -12x2 = 28x + 12x2 + -28x + -12x2

Combine like terms: -24x + -28x = -52x
-52x + 3x2 + -12x2 = 28x + 12x2 + -28x + -12x2

Combine like terms: 3x2 + -12x2 = -9x2
-52x + -9x2 = 28x + 12x2 + -28x + -12x2

Reorder the terms:
-52x + -9x2 = 28x + -28x + 12x2 + -12x2

Combine like terms: 28x + -28x = 0
-52x + -9x2 = 0 + 12x2 + -12x2
-52x + -9x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-52x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(52 + 9x) = 0

Ignore the factor -1.

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 '(52 + 9x)' equal to zero and attempt to solve:

Simplifying
52 + 9x = 0

Solving
52 + 9x = 0

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

Add '-52' to each side of the equation.
52 + -52 + 9x = 0 + -52

Combine like terms: 52 + -52 = 0
0 + 9x = 0 + -52
9x = 0 + -52

Combine like terms: 0 + -52 = -52
9x = -52

Divide each side by '9'.
x = -5.777777778

Simplifying
x = -5.777777778
Solution
x = {0, -5.777777778}

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