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

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

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

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

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

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

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) = (x + -2)(x + -2) + (x + 5)(x + 5)

Reorder the terms:
9 + -12x + 4x2 = (-2 + x)(x + -2) + (x + 5)(x + 5)

Reorder the terms:
9 + -12x + 4x2 = (-2 + x)(-2 + x) + (x + 5)(x + 5)

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

Combine like terms: -2x + -2x = -4x
9 + -12x + 4x2 = (4 + -4x + x2) + (x + 5)(x + 5)

Reorder the terms:
9 + -12x + 4x2 = 4 + -4x + x2 + (5 + x)(x + 5)

Reorder the terms:
9 + -12x + 4x2 = 4 + -4x + x2 + (5 + x)(5 + x)

Multiply (5 + x) * (5 + x)
9 + -12x + 4x2 = 4 + -4x + x2 + (5(5 + x) + x(5 + x))
9 + -12x + 4x2 = 4 + -4x + x2 + ((5 * 5 + x * 5) + x(5 + x))
9 + -12x + 4x2 = 4 + -4x + x2 + ((25 + 5x) + x(5 + x))
9 + -12x + 4x2 = 4 + -4x + x2 + (25 + 5x + (5 * x + x * x))
9 + -12x + 4x2 = 4 + -4x + x2 + (25 + 5x + (5x + x2))

Combine like terms: 5x + 5x = 10x
9 + -12x + 4x2 = 4 + -4x + x2 + (25 + 10x + x2)

Reorder the terms:
9 + -12x + 4x2 = 4 + 25 + -4x + 10x + x2 + x2

Combine like terms: 4 + 25 = 29
9 + -12x + 4x2 = 29 + -4x + 10x + x2 + x2

Combine like terms: -4x + 10x = 6x
9 + -12x + 4x2 = 29 + 6x + x2 + x2

Combine like terms: x2 + x2 = 2x2
9 + -12x + 4x2 = 29 + 6x + 2x2

Solving
9 + -12x + 4x2 = 29 + 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
9 + -29 + -12x + -6x + 4x2 + -2x2 = 29 + 6x + 2x2 + -29 + -6x + -2x2

Combine like terms: 9 + -29 = -20
-20 + -12x + -6x + 4x2 + -2x2 = 29 + 6x + 2x2 + -29 + -6x + -2x2

Combine like terms: -12x + -6x = -18x
-20 + -18x + 4x2 + -2x2 = 29 + 6x + 2x2 + -29 + -6x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
-20 + -18x + 2x2 = 29 + 6x + 2x2 + -29 + -6x + -2x2

Reorder the terms:
-20 + -18x + 2x2 = 29 + -29 + 6x + -6x + 2x2 + -2x2

Combine like terms: 29 + -29 = 0
-20 + -18x + 2x2 = 0 + 6x + -6x + 2x2 + -2x2
-20 + -18x + 2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
-20 + -18x + 2x2 = 0 + 2x2 + -2x2
-20 + -18x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-20 + -18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -9x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(10 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-1, 10}