1(4x-5)+1(2x+3)=3(2x+3)(4x-5)

Solution for 1(4x-5)+1(2x+3)=3(2x+3)(4x-5) equation:

Simplifying
1(4x + -5) + 1(2x + 3) = 3(2x + 3)(4x + -5)

Reorder the terms:
1(-5 + 4x) + 1(2x + 3) = 3(2x + 3)(4x + -5)
(-5 * 1 + 4x * 1) + 1(2x + 3) = 3(2x + 3)(4x + -5)
(-5 + 4x) + 1(2x + 3) = 3(2x + 3)(4x + -5)

Reorder the terms:
-5 + 4x + 1(3 + 2x) = 3(2x + 3)(4x + -5)
-5 + 4x + (3 * 1 + 2x * 1) = 3(2x + 3)(4x + -5)
-5 + 4x + (3 + 2x) = 3(2x + 3)(4x + -5)

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

Combine like terms: -5 + 3 = -2
-2 + 4x + 2x = 3(2x + 3)(4x + -5)

Combine like terms: 4x + 2x = 6x
-2 + 6x = 3(2x + 3)(4x + -5)

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

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

Multiply (3 + 2x) * (-5 + 4x)
-2 + 6x = 3(3(-5 + 4x) + 2x * (-5 + 4x))
-2 + 6x = 3((-5 * 3 + 4x * 3) + 2x * (-5 + 4x))
-2 + 6x = 3((-15 + 12x) + 2x * (-5 + 4x))
-2 + 6x = 3(-15 + 12x + (-5 * 2x + 4x * 2x))
-2 + 6x = 3(-15 + 12x + (-10x + 8x2))

Combine like terms: 12x + -10x = 2x
-2 + 6x = 3(-15 + 2x + 8x2)
-2 + 6x = (-15 * 3 + 2x * 3 + 8x2 * 3)
-2 + 6x = (-45 + 6x + 24x2)

Add '-6x' to each side of the equation.
-2 + 6x + -6x = -45 + 6x + -6x + 24x2

Combine like terms: 6x + -6x = 0
-2 + 0 = -45 + 6x + -6x + 24x2
-2 = -45 + 6x + -6x + 24x2

Combine like terms: 6x + -6x = 0
-2 = -45 + 0 + 24x2
-2 = -45 + 24x2

Solving
-2 = -45 + 24x2

Solving for variable 'x'.

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

Add '-24x2' to each side of the equation.
-2 + -24x2 = -45 + 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
-2 + -24x2 = -45 + 0
-2 + -24x2 = -45

Add '2' to each side of the equation.
-2 + 2 + -24x2 = -45 + 2

Combine like terms: -2 + 2 = 0
0 + -24x2 = -45 + 2
-24x2 = -45 + 2

Combine like terms: -45 + 2 = -43
-24x2 = -43

Divide each side by '-24'.
x2 = 1.791666667

Simplifying
x2 = 1.791666667

Take the square root of each side:
x = {-1.338531534, 1.338531534}