4w+3=(7w-6)(7w-6)

Solution for 4w+3=(7w-6)(7w-6) equation:

Simplifying
4w + 3 = (7w + -6)(7w + -6)

Reorder the terms:
3 + 4w = (7w + -6)(7w + -6)

Reorder the terms:
3 + 4w = (-6 + 7w)(7w + -6)

Reorder the terms:
3 + 4w = (-6 + 7w)(-6 + 7w)

Multiply (-6 + 7w) * (-6 + 7w)
3 + 4w = (-6(-6 + 7w) + 7w * (-6 + 7w))
3 + 4w = ((-6 * -6 + 7w * -6) + 7w * (-6 + 7w))
3 + 4w = ((36 + -42w) + 7w * (-6 + 7w))
3 + 4w = (36 + -42w + (-6 * 7w + 7w * 7w))
3 + 4w = (36 + -42w + (-42w + 49w2))

Combine like terms: -42w + -42w = -84w
3 + 4w = (36 + -84w + 49w2)

Solving
3 + 4w = 36 + -84w + 49w2

Solving for variable 'w'.

Reorder the terms:
3 + -36 + 4w + 84w + -49w2 = 36 + -84w + 49w2 + -36 + 84w + -49w2

Combine like terms: 3 + -36 = -33
-33 + 4w + 84w + -49w2 = 36 + -84w + 49w2 + -36 + 84w + -49w2

Combine like terms: 4w + 84w = 88w
-33 + 88w + -49w2 = 36 + -84w + 49w2 + -36 + 84w + -49w2

Reorder the terms:
-33 + 88w + -49w2 = 36 + -36 + -84w + 84w + 49w2 + -49w2

Combine like terms: 36 + -36 = 0
-33 + 88w + -49w2 = 0 + -84w + 84w + 49w2 + -49w2
-33 + 88w + -49w2 = -84w + 84w + 49w2 + -49w2

Combine like terms: -84w + 84w = 0
-33 + 88w + -49w2 = 0 + 49w2 + -49w2
-33 + 88w + -49w2 = 49w2 + -49w2

Combine like terms: 49w2 + -49w2 = 0
-33 + 88w + -49w2 = 0

Begin completing the square.  Divide all terms by
-49 the coefficient of the squared term: 

Divide each side by '-49'.
0.6734693878 + -1.795918367w + w2 = 0

Move the constant term to the right:

Add '-0.6734693878' to each side of the equation.
0.6734693878 + -1.795918367w + -0.6734693878 + w2 = 0 + -0.6734693878

Reorder the terms:
0.6734693878 + -0.6734693878 + -1.795918367w + w2 = 0 + -0.6734693878

Combine like terms: 0.6734693878 + -0.6734693878 = 0.0000000000
0.0000000000 + -1.795918367w + w2 = 0 + -0.6734693878
-1.795918367w + w2 = 0 + -0.6734693878

Combine like terms: 0 + -0.6734693878 = -0.6734693878
-1.795918367w + w2 = -0.6734693878

The w term is -1.795918367w.  Take half its coefficient (-0.8979591835).
Square it (0.8063306952) and add it to both sides.

Add '0.8063306952' to each side of the equation.
-1.795918367w + 0.8063306952 + w2 = -0.6734693878 + 0.8063306952

Reorder the terms:
0.8063306952 + -1.795918367w + w2 = -0.6734693878 + 0.8063306952

Combine like terms: -0.6734693878 + 0.8063306952 = 0.1328613074
0.8063306952 + -1.795918367w + w2 = 0.1328613074

Factor a perfect square on the left side:
(w + -0.8979591835)(w + -0.8979591835) = 0.1328613074

Calculate the square root of the right side: 0.36450145

Break this problem into two subproblems by setting 
(w + -0.8979591835) equal to 0.36450145 and -0.36450145.

Subproblem 1
w + -0.8979591835 = 0.36450145

Simplifying
w + -0.8979591835 = 0.36450145

Reorder the terms:
-0.8979591835 + w = 0.36450145

Solving
-0.8979591835 + w = 0.36450145

Solving for variable 'w'.

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

Add '0.8979591835' to each side of the equation.
-0.8979591835 + 0.8979591835 + w = 0.36450145 + 0.8979591835

Combine like terms: -0.8979591835 + 0.8979591835 = 0.0000000000
0.0000000000 + w = 0.36450145 + 0.8979591835
w = 0.36450145 + 0.8979591835

Combine like terms: 0.36450145 + 0.8979591835 = 1.2624606335
w = 1.2624606335

Simplifying
w = 1.2624606335

Subproblem 2
w + -0.8979591835 = -0.36450145

Simplifying
w + -0.8979591835 = -0.36450145

Reorder the terms:
-0.8979591835 + w = -0.36450145

Solving
-0.8979591835 + w = -0.36450145

Solving for variable 'w'.

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

Add '0.8979591835' to each side of the equation.
-0.8979591835 + 0.8979591835 + w = -0.36450145 + 0.8979591835

Combine like terms: -0.8979591835 + 0.8979591835 = 0.0000000000
0.0000000000 + w = -0.36450145 + 0.8979591835
w = -0.36450145 + 0.8979591835

Combine like terms: -0.36450145 + 0.8979591835 = 0.5334577335
w = 0.5334577335

Simplifying
w = 0.5334577335

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.2624606335, 0.5334577335}