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

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


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

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

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

Multiply (-4 + 3x) * (-4 + 3x)
(-4(-4 + 3x) + 3x * (-4 + 3x)) = (x + 1)(x + 1)
((-4 * -4 + 3x * -4) + 3x * (-4 + 3x)) = (x + 1)(x + 1)
((16 + -12x) + 3x * (-4 + 3x)) = (x + 1)(x + 1)
(16 + -12x + (-4 * 3x + 3x * 3x)) = (x + 1)(x + 1)
(16 + -12x + (-12x + 9x2)) = (x + 1)(x + 1)

Combine like terms: -12x + -12x = -24x
(16 + -24x + 9x2) = (x + 1)(x + 1)

Reorder the terms:
16 + -24x + 9x2 = (1 + x)(x + 1)

Reorder the terms:
16 + -24x + 9x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
16 + -24x + 9x2 = (1(1 + x) + x(1 + x))
16 + -24x + 9x2 = ((1 * 1 + x * 1) + x(1 + x))
16 + -24x + 9x2 = ((1 + 1x) + x(1 + x))
16 + -24x + 9x2 = (1 + 1x + (1 * x + x * x))
16 + -24x + 9x2 = (1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
16 + -24x + 9x2 = (1 + 2x + x2)

Solving
16 + -24x + 9x2 = 1 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
16 + -1 + -24x + -2x + 9x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 16 + -1 = 15
15 + -24x + -2x + 9x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: -24x + -2x = -26x
15 + -26x + 9x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 9x2 + -1x2 = 8x2
15 + -26x + 8x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
15 + -26x + 8x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
15 + -26x + 8x2 = 0 + 2x + -2x + x2 + -1x2
15 + -26x + 8x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
15 + -26x + 8x2 = 0 + x2 + -1x2
15 + -26x + 8x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + -26x + 8x2 = 0

Factor a trinomial.
(3 + -4x)(5 + -2x) = 0


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0.75, 2.5}

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