(2x-5)+1=7x(-3x)+15

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Solution for (2x-5)+1=7x(-3x)+15 equation: 


Simplifying
(2x + -5) + 1 = 7x(-3x) + 15

Reorder the terms:
(-5 + 2x) + 1 = 7x(-3x) + 15

Remove parenthesis around (-5 + 2x)
-5 + 2x + 1 = 7x(-3x) + 15

Reorder the terms:
-5 + 1 + 2x = 7x(-3x) + 15

Combine like terms: -5 + 1 = -4
-4 + 2x = 7x(-3x) + 15

Remove parenthesis around (-3x)
-4 + 2x = 7x * -3x + 15

Reorder the terms for easier multiplication:
-4 + 2x = 7 * -3x * x + 15

Multiply 7 * -3
-4 + 2x = -21x * x + 15

Multiply x * x
-4 + 2x = -21x2 + 15

Reorder the terms:
-4 + 2x = 15 + -21x2

Solving
-4 + 2x = 15 + -21x2

Solving for variable 'x'.

Reorder the terms:
-4 + -15 + 2x + 21x2 = 15 + -21x2 + -15 + 21x2

Combine like terms: -4 + -15 = -19
-19 + 2x + 21x2 = 15 + -21x2 + -15 + 21x2

Reorder the terms:
-19 + 2x + 21x2 = 15 + -15 + -21x2 + 21x2

Combine like terms: 15 + -15 = 0
-19 + 2x + 21x2 = 0 + -21x2 + 21x2
-19 + 2x + 21x2 = -21x2 + 21x2

Combine like terms: -21x2 + 21x2 = 0
-19 + 2x + 21x2 = 0

Factor a trinomial.
(-1 + -1x)(19 + -21x) = 0


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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(19 + -21x)' equal to zero and attempt to solve:

Simplifying
19 + -21x = 0

Solving
19 + -21x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-19' to each side of the equation.
19 + -19 + -21x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -21x = 0 + -19
-21x = 0 + -19

Combine like terms: 0 + -19 = -19
-21x = -19

Divide each side by '-21'.
x = 0.9047619048

Simplifying
x = 0.9047619048
Solution
x = {-1, 0.9047619048}

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