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

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


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

Reorder the terms:
(-4 + 3x)(5x + 2) = (3x + -4)(3 + -2x)

Reorder the terms:
(-4 + 3x)(2 + 5x) = (3x + -4)(3 + -2x)

Multiply (-4 + 3x) * (2 + 5x)
(-4(2 + 5x) + 3x * (2 + 5x)) = (3x + -4)(3 + -2x)
((2 * -4 + 5x * -4) + 3x * (2 + 5x)) = (3x + -4)(3 + -2x)
((-8 + -20x) + 3x * (2 + 5x)) = (3x + -4)(3 + -2x)
(-8 + -20x + (2 * 3x + 5x * 3x)) = (3x + -4)(3 + -2x)
(-8 + -20x + (6x + 15x2)) = (3x + -4)(3 + -2x)

Combine like terms: -20x + 6x = -14x
(-8 + -14x + 15x2) = (3x + -4)(3 + -2x)

Reorder the terms:
-8 + -14x + 15x2 = (-4 + 3x)(3 + -2x)

Multiply (-4 + 3x) * (3 + -2x)
-8 + -14x + 15x2 = (-4(3 + -2x) + 3x * (3 + -2x))
-8 + -14x + 15x2 = ((3 * -4 + -2x * -4) + 3x * (3 + -2x))
-8 + -14x + 15x2 = ((-12 + 8x) + 3x * (3 + -2x))
-8 + -14x + 15x2 = (-12 + 8x + (3 * 3x + -2x * 3x))
-8 + -14x + 15x2 = (-12 + 8x + (9x + -6x2))

Combine like terms: 8x + 9x = 17x
-8 + -14x + 15x2 = (-12 + 17x + -6x2)

Solving
-8 + -14x + 15x2 = -12 + 17x + -6x2

Solving for variable 'x'.

Reorder the terms:
-8 + 12 + -14x + -17x + 15x2 + 6x2 = -12 + 17x + -6x2 + 12 + -17x + 6x2

Combine like terms: -8 + 12 = 4
4 + -14x + -17x + 15x2 + 6x2 = -12 + 17x + -6x2 + 12 + -17x + 6x2

Combine like terms: -14x + -17x = -31x
4 + -31x + 15x2 + 6x2 = -12 + 17x + -6x2 + 12 + -17x + 6x2

Combine like terms: 15x2 + 6x2 = 21x2
4 + -31x + 21x2 = -12 + 17x + -6x2 + 12 + -17x + 6x2

Reorder the terms:
4 + -31x + 21x2 = -12 + 12 + 17x + -17x + -6x2 + 6x2

Combine like terms: -12 + 12 = 0
4 + -31x + 21x2 = 0 + 17x + -17x + -6x2 + 6x2
4 + -31x + 21x2 = 17x + -17x + -6x2 + 6x2

Combine like terms: 17x + -17x = 0
4 + -31x + 21x2 = 0 + -6x2 + 6x2
4 + -31x + 21x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
4 + -31x + 21x2 = 0

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


Subproblem 1
Set the factor '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429

Subproblem 2
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
Solution
x = {0.1428571429, 1.333333333}

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