(7x+10)(7x-10)=49x-100

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Solution for (7x+10)(7x-10)=49x-100 equation: 


Simplifying
(7x + 10)(7x + -10) = 49x + -100

Reorder the terms:
(10 + 7x)(7x + -10) = 49x + -100

Reorder the terms:
(10 + 7x)(-10 + 7x) = 49x + -100

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

Combine like terms: 70x + -70x = 0
(-100 + 0 + 49x2) = 49x + -100
(-100 + 49x2) = 49x + -100

Reorder the terms:
-100 + 49x2 = -100 + 49x

Add '100' to each side of the equation.
-100 + 100 + 49x2 = -100 + 100 + 49x

Combine like terms: -100 + 100 = 0
0 + 49x2 = -100 + 100 + 49x
49x2 = -100 + 100 + 49x

Combine like terms: -100 + 100 = 0
49x2 = 0 + 49x
49x2 = 49x

Solving
49x2 = 49x

Solving for variable 'x'.

Reorder the terms:
-49x + 49x2 = 49x + -49x

Combine like terms: 49x + -49x = 0
-49x + 49x2 = 0

Factor out the Greatest Common Factor (GCF), '49x'.
49x(-1 + x) = 0

Ignore the factor 49.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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