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

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


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

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

Reorder the terms:
-6x + 2x2 = 7(-3 + x)
-6x + 2x2 = (-3 * 7 + x * 7)
-6x + 2x2 = (-21 + 7x)

Solving
-6x + 2x2 = -21 + 7x

Solving for variable 'x'.

Reorder the terms:
21 + -6x + -7x + 2x2 = -21 + 7x + 21 + -7x

Combine like terms: -6x + -7x = -13x
21 + -13x + 2x2 = -21 + 7x + 21 + -7x

Reorder the terms:
21 + -13x + 2x2 = -21 + 21 + 7x + -7x

Combine like terms: -21 + 21 = 0
21 + -13x + 2x2 = 0 + 7x + -7x
21 + -13x + 2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
21 + -13x + 2x2 = 0

Factor a trinomial.
(3 + -1x)(7 + -2x) = 0


Subproblem 1
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

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {3, 3.5}

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