5x(x-5)=6(2-7x)

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Solution for 5x(x-5)=6(2-7x) equation: 


Simplifying
5x(x + -5) = 6(2 + -7x)

Reorder the terms:
5x(-5 + x) = 6(2 + -7x)
(-5 * 5x + x * 5x) = 6(2 + -7x)
(-25x + 5x2) = 6(2 + -7x)
-25x + 5x2 = (2 * 6 + -7x * 6)
-25x + 5x2 = (12 + -42x)

Solving
-25x + 5x2 = 12 + -42x

Solving for variable 'x'.

Reorder the terms:
-12 + -25x + 42x + 5x2 = 12 + -42x + -12 + 42x

Combine like terms: -25x + 42x = 17x
-12 + 17x + 5x2 = 12 + -42x + -12 + 42x

Reorder the terms:
-12 + 17x + 5x2 = 12 + -12 + -42x + 42x

Combine like terms: 12 + -12 = 0
-12 + 17x + 5x2 = 0 + -42x + 42x
-12 + 17x + 5x2 = -42x + 42x

Combine like terms: -42x + 42x = 0
-12 + 17x + 5x2 = 0

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


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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-4, 0.6}

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