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

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


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

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

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

Combine like terms: 4x + 4x = 8x
-2 + 8x = 3(4x + 3)(4x + -5)

Reorder the terms:
-2 + 8x = 3(3 + 4x)(4x + -5)

Reorder the terms:
-2 + 8x = 3(3 + 4x)(-5 + 4x)

Multiply (3 + 4x) * (-5 + 4x)
-2 + 8x = 3(3(-5 + 4x) + 4x * (-5 + 4x))
-2 + 8x = 3((-5 * 3 + 4x * 3) + 4x * (-5 + 4x))
-2 + 8x = 3((-15 + 12x) + 4x * (-5 + 4x))
-2 + 8x = 3(-15 + 12x + (-5 * 4x + 4x * 4x))
-2 + 8x = 3(-15 + 12x + (-20x + 16x2))

Combine like terms: 12x + -20x = -8x
-2 + 8x = 3(-15 + -8x + 16x2)
-2 + 8x = (-15 * 3 + -8x * 3 + 16x2 * 3)
-2 + 8x = (-45 + -24x + 48x2)

Solving
-2 + 8x = -45 + -24x + 48x2

Solving for variable 'x'.

Reorder the terms:
-2 + 45 + 8x + 24x + -48x2 = -45 + -24x + 48x2 + 45 + 24x + -48x2

Combine like terms: -2 + 45 = 43
43 + 8x + 24x + -48x2 = -45 + -24x + 48x2 + 45 + 24x + -48x2

Combine like terms: 8x + 24x = 32x
43 + 32x + -48x2 = -45 + -24x + 48x2 + 45 + 24x + -48x2

Reorder the terms:
43 + 32x + -48x2 = -45 + 45 + -24x + 24x + 48x2 + -48x2

Combine like terms: -45 + 45 = 0
43 + 32x + -48x2 = 0 + -24x + 24x + 48x2 + -48x2
43 + 32x + -48x2 = -24x + 24x + 48x2 + -48x2

Combine like terms: -24x + 24x = 0
43 + 32x + -48x2 = 0 + 48x2 + -48x2
43 + 32x + -48x2 = 48x2 + -48x2

Combine like terms: 48x2 + -48x2 = 0
43 + 32x + -48x2 = 0

Begin completing the square.  Divide all terms by
-48 the coefficient of the squared term: 

Divide each side by '-48'.
-0.8958333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.8958333333' to each side of the equation.
-0.8958333333 + -0.6666666667x + 0.8958333333 + x2 = 0 + 0.8958333333

Reorder the terms:
-0.8958333333 + 0.8958333333 + -0.6666666667x + x2 = 0 + 0.8958333333

Combine like terms: -0.8958333333 + 0.8958333333 = 0.0000000000
0.0000000000 + -0.6666666667x + x2 = 0 + 0.8958333333
-0.6666666667x + x2 = 0 + 0.8958333333

Combine like terms: 0 + 0.8958333333 = 0.8958333333
-0.6666666667x + x2 = 0.8958333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 0.8958333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 0.8958333333 + 0.1111111112

Combine like terms: 0.8958333333 + 0.1111111112 = 1.0069444445
0.1111111112 + -0.6666666667x + x2 = 1.0069444445

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 1.0069444445

Calculate the square root of the right side: 1.003466215

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.003466215 and -1.003466215.

Subproblem 1

x + -0.3333333334 = 1.003466215 Simplifying x + -0.3333333334 = 1.003466215 Reorder the terms: -0.3333333334 + x = 1.003466215 Solving -0.3333333334 + x = 1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 1.003466215 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.003466215 + 0.3333333334 x = 1.003466215 + 0.3333333334 Combine like terms: 1.003466215 + 0.3333333334 = 1.3367995484 x = 1.3367995484 Simplifying x = 1.3367995484

Subproblem 2

x + -0.3333333334 = -1.003466215 Simplifying x + -0.3333333334 = -1.003466215 Reorder the terms: -0.3333333334 + x = -1.003466215 Solving -0.3333333334 + x = -1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -1.003466215 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.003466215 + 0.3333333334 x = -1.003466215 + 0.3333333334 Combine like terms: -1.003466215 + 0.3333333334 = -0.6701328816 x = -0.6701328816 Simplifying x = -0.6701328816

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.3367995484, -0.6701328816}

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