7x^2+7x-25=5x-1+6x^2

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Solution for 7x^2+7x-25=5x-1+6x^2 equation:


Simplifying
7x2 + 7x + -25 = 5x + -1 + 6x2

Reorder the terms:
-25 + 7x + 7x2 = 5x + -1 + 6x2

Reorder the terms:
-25 + 7x + 7x2 = -1 + 5x + 6x2

Solving
-25 + 7x + 7x2 = -1 + 5x + 6x2

Solving for variable 'x'.

Reorder the terms:
-25 + 1 + 7x + -5x + 7x2 + -6x2 = -1 + 5x + 6x2 + 1 + -5x + -6x2

Combine like terms: -25 + 1 = -24
-24 + 7x + -5x + 7x2 + -6x2 = -1 + 5x + 6x2 + 1 + -5x + -6x2

Combine like terms: 7x + -5x = 2x
-24 + 2x + 7x2 + -6x2 = -1 + 5x + 6x2 + 1 + -5x + -6x2

Combine like terms: 7x2 + -6x2 = 1x2
-24 + 2x + 1x2 = -1 + 5x + 6x2 + 1 + -5x + -6x2

Reorder the terms:
-24 + 2x + 1x2 = -1 + 1 + 5x + -5x + 6x2 + -6x2

Combine like terms: -1 + 1 = 0
-24 + 2x + 1x2 = 0 + 5x + -5x + 6x2 + -6x2
-24 + 2x + 1x2 = 5x + -5x + 6x2 + -6x2

Combine like terms: 5x + -5x = 0
-24 + 2x + 1x2 = 0 + 6x2 + -6x2
-24 + 2x + 1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-24 + 2x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
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
Solution
x = {-6, 4}

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