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

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


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

Reorder the terms:
2(5 + x) + -7 = 3x(x + -2)
(5 * 2 + x * 2) + -7 = 3x(x + -2)
(10 + 2x) + -7 = 3x(x + -2)

Reorder the terms:
10 + -7 + 2x = 3x(x + -2)

Combine like terms: 10 + -7 = 3
3 + 2x = 3x(x + -2)

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

Solving
3 + 2x = -6x + 3x2

Solving for variable 'x'.

Combine like terms: 2x + 6x = 8x
3 + 8x + -3x2 = -6x + 3x2 + 6x + -3x2

Reorder the terms:
3 + 8x + -3x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
3 + 8x + -3x2 = 0 + 3x2 + -3x2
3 + 8x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
3 + 8x + -3x2 = 0

Factor a trinomial.
(3 + -1x)(1 + 3x) = 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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {3, -0.3333333333}

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