(7x)(5x+5)=(10)(16x-6)

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Solution for (7x)(5x+5)=(10)(16x-6) equation: 


Simplifying
(7x)(5x + 5) = (10)(16x + -6)

Remove parenthesis around (7x)
7x(5x + 5) = (10)(16x + -6)

Reorder the terms:
7x(5 + 5x) = (10)(16x + -6)
(5 * 7x + 5x * 7x) = (10)(16x + -6)
(35x + 35x2) = (10)(16x + -6)

Reorder the terms:
35x + 35x2 = 10(-6 + 16x)
35x + 35x2 = (-6 * 10 + 16x * 10)
35x + 35x2 = (-60 + 160x)

Solving
35x + 35x2 = -60 + 160x

Solving for variable 'x'.

Reorder the terms:
60 + 35x + -160x + 35x2 = -60 + 160x + 60 + -160x

Combine like terms: 35x + -160x = -125x
60 + -125x + 35x2 = -60 + 160x + 60 + -160x

Reorder the terms:
60 + -125x + 35x2 = -60 + 60 + 160x + -160x

Combine like terms: -60 + 60 = 0
60 + -125x + 35x2 = 0 + 160x + -160x
60 + -125x + 35x2 = 160x + -160x

Combine like terms: 160x + -160x = 0
60 + -125x + 35x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(12 + -25x + 7x2) = 0

Factor a trinomial.
5((4 + -7x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + -7x)' equal to zero and attempt to solve:

Simplifying
4 + -7x = 0

Solving
4 + -7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = 0 + -4
-7x = 0 + -4

Combine like terms: 0 + -4 = -4
-7x = -4

Divide each side by '-7'.
x = 0.5714285714

Simplifying
x = 0.5714285714

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.5714285714, 3}

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