2x(5x-7)=2x^2-5

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


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

Reorder the terms:
2x(-7 + 5x) = 2x2 + -5
(-7 * 2x + 5x * 2x) = 2x2 + -5
(-14x + 10x2) = 2x2 + -5

Reorder the terms:
-14x + 10x2 = -5 + 2x2

Solving
-14x + 10x2 = -5 + 2x2

Solving for variable 'x'.

Reorder the terms:
5 + -14x + 10x2 + -2x2 = -5 + 2x2 + 5 + -2x2

Combine like terms: 10x2 + -2x2 = 8x2
5 + -14x + 8x2 = -5 + 2x2 + 5 + -2x2

Reorder the terms:
5 + -14x + 8x2 = -5 + 5 + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
5 + -14x + 8x2 = 0 + 2x2 + -2x2
5 + -14x + 8x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + -14x + 8x2 = 0

Factor a trinomial.
(1 + -2x)(5 + -4x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {0.5, 1.25}

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