2x(3x-7)=5(7-3x)

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


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

Reorder the terms:
2x(-7 + 3x) = 5(7 + -3x)
(-7 * 2x + 3x * 2x) = 5(7 + -3x)
(-14x + 6x2) = 5(7 + -3x)
-14x + 6x2 = (7 * 5 + -3x * 5)
-14x + 6x2 = (35 + -15x)

Solving
-14x + 6x2 = 35 + -15x

Solving for variable 'x'.

Reorder the terms:
-35 + -14x + 15x + 6x2 = 35 + -15x + -35 + 15x

Combine like terms: -14x + 15x = 1x
-35 + 1x + 6x2 = 35 + -15x + -35 + 15x

Reorder the terms:
-35 + 1x + 6x2 = 35 + -35 + -15x + 15x

Combine like terms: 35 + -35 = 0
-35 + 1x + 6x2 = 0 + -15x + 15x
-35 + 1x + 6x2 = -15x + 15x

Combine like terms: -15x + 15x = 0
-35 + 1x + 6x2 = 0

Factor a trinomial.
(-5 + -2x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-2.5, 2.333333333}

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