(3x+7)(3x+7)=(7x-10)(7x-10)

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Solution for (3x+7)(3x+7)=(7x-10)(7x-10) equation: 


Simplifying
(3x + 7)(3x + 7) = (7x + -10)(7x + -10)

Reorder the terms:
(7 + 3x)(3x + 7) = (7x + -10)(7x + -10)

Reorder the terms:
(7 + 3x)(7 + 3x) = (7x + -10)(7x + -10)

Multiply (7 + 3x) * (7 + 3x)
(7(7 + 3x) + 3x * (7 + 3x)) = (7x + -10)(7x + -10)
((7 * 7 + 3x * 7) + 3x * (7 + 3x)) = (7x + -10)(7x + -10)
((49 + 21x) + 3x * (7 + 3x)) = (7x + -10)(7x + -10)
(49 + 21x + (7 * 3x + 3x * 3x)) = (7x + -10)(7x + -10)
(49 + 21x + (21x + 9x2)) = (7x + -10)(7x + -10)

Combine like terms: 21x + 21x = 42x
(49 + 42x + 9x2) = (7x + -10)(7x + -10)

Reorder the terms:
49 + 42x + 9x2 = (-10 + 7x)(7x + -10)

Reorder the terms:
49 + 42x + 9x2 = (-10 + 7x)(-10 + 7x)

Multiply (-10 + 7x) * (-10 + 7x)
49 + 42x + 9x2 = (-10(-10 + 7x) + 7x * (-10 + 7x))
49 + 42x + 9x2 = ((-10 * -10 + 7x * -10) + 7x * (-10 + 7x))
49 + 42x + 9x2 = ((100 + -70x) + 7x * (-10 + 7x))
49 + 42x + 9x2 = (100 + -70x + (-10 * 7x + 7x * 7x))
49 + 42x + 9x2 = (100 + -70x + (-70x + 49x2))

Combine like terms: -70x + -70x = -140x
49 + 42x + 9x2 = (100 + -140x + 49x2)

Solving
49 + 42x + 9x2 = 100 + -140x + 49x2

Solving for variable 'x'.

Reorder the terms:
49 + -100 + 42x + 140x + 9x2 + -49x2 = 100 + -140x + 49x2 + -100 + 140x + -49x2

Combine like terms: 49 + -100 = -51
-51 + 42x + 140x + 9x2 + -49x2 = 100 + -140x + 49x2 + -100 + 140x + -49x2

Combine like terms: 42x + 140x = 182x
-51 + 182x + 9x2 + -49x2 = 100 + -140x + 49x2 + -100 + 140x + -49x2

Combine like terms: 9x2 + -49x2 = -40x2
-51 + 182x + -40x2 = 100 + -140x + 49x2 + -100 + 140x + -49x2

Reorder the terms:
-51 + 182x + -40x2 = 100 + -100 + -140x + 140x + 49x2 + -49x2

Combine like terms: 100 + -100 = 0
-51 + 182x + -40x2 = 0 + -140x + 140x + 49x2 + -49x2
-51 + 182x + -40x2 = -140x + 140x + 49x2 + -49x2

Combine like terms: -140x + 140x = 0
-51 + 182x + -40x2 = 0 + 49x2 + -49x2
-51 + 182x + -40x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
-51 + 182x + -40x2 = 0

Factor a trinomial.
(-17 + 4x)(3 + -10x) = 0


Subproblem 1
Set the factor '(-17 + 4x)' equal to zero and attempt to solve:

Simplifying
-17 + 4x = 0

Solving
-17 + 4x = 0

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

Add '17' to each side of the equation.
-17 + 17 + 4x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 4x = 0 + 17
4x = 0 + 17

Combine like terms: 0 + 17 = 17
4x = 17

Divide each side by '4'.
x = 4.25

Simplifying
x = 4.25

Subproblem 2
Set the factor '(3 + -10x)' equal to zero and attempt to solve:

Simplifying
3 + -10x = 0

Solving
3 + -10x = 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 + -10x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -10x = 0 + -3
-10x = 0 + -3

Combine like terms: 0 + -3 = -3
-10x = -3

Divide each side by '-10'.
x = 0.3

Simplifying
x = 0.3
Solution
x = {4.25, 0.3}

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