12x^2+28x-5=2x+5

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Solution for 12x^2+28x-5=2x+5 equation:


Simplifying
12x2 + 28x + -5 = 2x + 5

Reorder the terms:
-5 + 28x + 12x2 = 2x + 5

Reorder the terms:
-5 + 28x + 12x2 = 5 + 2x

Solving
-5 + 28x + 12x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
-5 + -5 + 28x + -2x + 12x2 = 5 + 2x + -5 + -2x

Combine like terms: -5 + -5 = -10
-10 + 28x + -2x + 12x2 = 5 + 2x + -5 + -2x

Combine like terms: 28x + -2x = 26x
-10 + 26x + 12x2 = 5 + 2x + -5 + -2x

Reorder the terms:
-10 + 26x + 12x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
-10 + 26x + 12x2 = 0 + 2x + -2x
-10 + 26x + 12x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-10 + 26x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 13x + 6x2) = 0

Factor a trinomial.
2((-5 + -2x)(1 + -3x)) = 0

Ignore the factor 2.

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 '(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 = {-2.5, 0.3333333333}

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