3x(2x-5)=4x(3x+7)

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Solution for 3x(2x-5)=4x(3x+7) equation: 


Simplifying
3x(2x + -5) = 4x(3x + 7)

Reorder the terms:
3x(-5 + 2x) = 4x(3x + 7)
(-5 * 3x + 2x * 3x) = 4x(3x + 7)
(-15x + 6x2) = 4x(3x + 7)

Reorder the terms:
-15x + 6x2 = 4x(7 + 3x)
-15x + 6x2 = (7 * 4x + 3x * 4x)
-15x + 6x2 = (28x + 12x2)

Solving
-15x + 6x2 = 28x + 12x2

Solving for variable 'x'.

Reorder the terms:
-15x + -28x + 6x2 + -12x2 = 28x + 12x2 + -28x + -12x2

Combine like terms: -15x + -28x = -43x
-43x + 6x2 + -12x2 = 28x + 12x2 + -28x + -12x2

Combine like terms: 6x2 + -12x2 = -6x2
-43x + -6x2 = 28x + 12x2 + -28x + -12x2

Reorder the terms:
-43x + -6x2 = 28x + -28x + 12x2 + -12x2

Combine like terms: 28x + -28x = 0
-43x + -6x2 = 0 + 12x2 + -12x2
-43x + -6x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-43x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(43 + 6x) = 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 '(43 + 6x)' equal to zero and attempt to solve:

Simplifying
43 + 6x = 0

Solving
43 + 6x = 0

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

Add '-43' to each side of the equation.
43 + -43 + 6x = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 6x = 0 + -43
6x = 0 + -43

Combine like terms: 0 + -43 = -43
6x = -43

Divide each side by '6'.
x = -7.166666667

Simplifying
x = -7.166666667
Solution
x = {0, -7.166666667}

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