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

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


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

Reorder the terms:
(-4 + 3x)(4x + 3) = (6x + 4)(2x + -5)

Reorder the terms:
(-4 + 3x)(3 + 4x) = (6x + 4)(2x + -5)

Multiply (-4 + 3x) * (3 + 4x)
(-4(3 + 4x) + 3x * (3 + 4x)) = (6x + 4)(2x + -5)
((3 * -4 + 4x * -4) + 3x * (3 + 4x)) = (6x + 4)(2x + -5)
((-12 + -16x) + 3x * (3 + 4x)) = (6x + 4)(2x + -5)
(-12 + -16x + (3 * 3x + 4x * 3x)) = (6x + 4)(2x + -5)
(-12 + -16x + (9x + 12x2)) = (6x + 4)(2x + -5)

Combine like terms: -16x + 9x = -7x
(-12 + -7x + 12x2) = (6x + 4)(2x + -5)

Reorder the terms:
-12 + -7x + 12x2 = (4 + 6x)(2x + -5)

Reorder the terms:
-12 + -7x + 12x2 = (4 + 6x)(-5 + 2x)

Multiply (4 + 6x) * (-5 + 2x)
-12 + -7x + 12x2 = (4(-5 + 2x) + 6x * (-5 + 2x))
-12 + -7x + 12x2 = ((-5 * 4 + 2x * 4) + 6x * (-5 + 2x))
-12 + -7x + 12x2 = ((-20 + 8x) + 6x * (-5 + 2x))
-12 + -7x + 12x2 = (-20 + 8x + (-5 * 6x + 2x * 6x))
-12 + -7x + 12x2 = (-20 + 8x + (-30x + 12x2))

Combine like terms: 8x + -30x = -22x
-12 + -7x + 12x2 = (-20 + -22x + 12x2)

Add '-12x2' to each side of the equation.
-12 + -7x + 12x2 + -12x2 = -20 + -22x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-12 + -7x + 0 = -20 + -22x + 12x2 + -12x2
-12 + -7x = -20 + -22x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-12 + -7x = -20 + -22x + 0
-12 + -7x = -20 + -22x

Solving
-12 + -7x = -20 + -22x

Solving for variable 'x'.

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

Add '22x' to each side of the equation.
-12 + -7x + 22x = -20 + -22x + 22x

Combine like terms: -7x + 22x = 15x
-12 + 15x = -20 + -22x + 22x

Combine like terms: -22x + 22x = 0
-12 + 15x = -20 + 0
-12 + 15x = -20

Add '12' to each side of the equation.
-12 + 12 + 15x = -20 + 12

Combine like terms: -12 + 12 = 0
0 + 15x = -20 + 12
15x = -20 + 12

Combine like terms: -20 + 12 = -8
15x = -8

Divide each side by '15'.
x = -0.5333333333

Simplifying
x = -0.5333333333

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