2x(6x+5)=5x(3-4x)

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Solution for 2x(6x+5)=5x(3-4x) equation: 


Simplifying
2x(6x + 5) = 5x(3 + -4x)

Reorder the terms:
2x(5 + 6x) = 5x(3 + -4x)
(5 * 2x + 6x * 2x) = 5x(3 + -4x)
(10x + 12x2) = 5x(3 + -4x)
10x + 12x2 = (3 * 5x + -4x * 5x)
10x + 12x2 = (15x + -20x2)

Solving
10x + 12x2 = 15x + -20x2

Solving for variable 'x'.

Reorder the terms:
10x + -15x + 12x2 + 20x2 = 15x + -20x2 + -15x + 20x2

Combine like terms: 10x + -15x = -5x
-5x + 12x2 + 20x2 = 15x + -20x2 + -15x + 20x2

Combine like terms: 12x2 + 20x2 = 32x2
-5x + 32x2 = 15x + -20x2 + -15x + 20x2

Reorder the terms:
-5x + 32x2 = 15x + -15x + -20x2 + 20x2

Combine like terms: 15x + -15x = 0
-5x + 32x2 = 0 + -20x2 + 20x2
-5x + 32x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
-5x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 32x) = 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 '(-5 + 32x)' equal to zero and attempt to solve:

Simplifying
-5 + 32x = 0

Solving
-5 + 32x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 32x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 32x = 0 + 5
32x = 0 + 5

Combine like terms: 0 + 5 = 5
32x = 5

Divide each side by '32'.
x = 0.15625

Simplifying
x = 0.15625
Solution
x = {0, 0.15625}

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