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

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

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

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

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

Multiply (-2 + -3x) * (3 + 4x)
(-2(3 + 4x) + -3x * (3 + 4x)) = (x + -5)(4x + 3)
((3 * -2 + 4x * -2) + -3x * (3 + 4x)) = (x + -5)(4x + 3)
((-6 + -8x) + -3x * (3 + 4x)) = (x + -5)(4x + 3)
(-6 + -8x + (3 * -3x + 4x * -3x)) = (x + -5)(4x + 3)
(-6 + -8x + (-9x + -12x2)) = (x + -5)(4x + 3)

Combine like terms: -8x + -9x = -17x
(-6 + -17x + -12x2) = (x + -5)(4x + 3)

Reorder the terms:
-6 + -17x + -12x2 = (-5 + x)(4x + 3)

Reorder the terms:
-6 + -17x + -12x2 = (-5 + x)(3 + 4x)

Multiply (-5 + x) * (3 + 4x)
-6 + -17x + -12x2 = (-5(3 + 4x) + x(3 + 4x))
-6 + -17x + -12x2 = ((3 * -5 + 4x * -5) + x(3 + 4x))
-6 + -17x + -12x2 = ((-15 + -20x) + x(3 + 4x))
-6 + -17x + -12x2 = (-15 + -20x + (3 * x + 4x * x))
-6 + -17x + -12x2 = (-15 + -20x + (3x + 4x2))

Combine like terms: -20x + 3x = -17x
-6 + -17x + -12x2 = (-15 + -17x + 4x2)

Add '17x' to each side of the equation.
-6 + -17x + 17x + -12x2 = -15 + -17x + 17x + 4x2

Combine like terms: -17x + 17x = 0
-6 + 0 + -12x2 = -15 + -17x + 17x + 4x2
-6 + -12x2 = -15 + -17x + 17x + 4x2

Combine like terms: -17x + 17x = 0
-6 + -12x2 = -15 + 0 + 4x2
-6 + -12x2 = -15 + 4x2

Solving
-6 + -12x2 = -15 + 4x2

Solving for variable 'x'.

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

Add '-4x2' to each side of the equation.
-6 + -12x2 + -4x2 = -15 + 4x2 + -4x2

Combine like terms: -12x2 + -4x2 = -16x2
-6 + -16x2 = -15 + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + -16x2 = -15 + 0
-6 + -16x2 = -15

Add '6' to each side of the equation.
-6 + 6 + -16x2 = -15 + 6

Combine like terms: -6 + 6 = 0
0 + -16x2 = -15 + 6
-16x2 = -15 + 6

Combine like terms: -15 + 6 = -9
-16x2 = -9

Divide each side by '-16'.
x2 = 0.5625

Simplifying
x2 = 0.5625

Take the square root of each side:
x = {-0.75, 0.75}