7(x^2-5)=2x(3x+1)

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Solution for 7(x^2-5)=2x(3x+1) equation: 


Simplifying
7(x2 + -5) = 2x(3x + 1)

Reorder the terms:
7(-5 + x2) = 2x(3x + 1)
(-5 * 7 + x2 * 7) = 2x(3x + 1)
(-35 + 7x2) = 2x(3x + 1)

Reorder the terms:
-35 + 7x2 = 2x(1 + 3x)
-35 + 7x2 = (1 * 2x + 3x * 2x)
-35 + 7x2 = (2x + 6x2)

Solving
-35 + 7x2 = 2x + 6x2

Solving for variable 'x'.

Reorder the terms:
-35 + -2x + 7x2 + -6x2 = 2x + 6x2 + -2x + -6x2

Combine like terms: 7x2 + -6x2 = 1x2
-35 + -2x + 1x2 = 2x + 6x2 + -2x + -6x2

Reorder the terms:
-35 + -2x + 1x2 = 2x + -2x + 6x2 + -6x2

Combine like terms: 2x + -2x = 0
-35 + -2x + 1x2 = 0 + 6x2 + -6x2
-35 + -2x + 1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-35 + -2x + 1x2 = 0

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


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-5, 7}

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