4x^2+13x-13=2(x-5)

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Solution for 4x^2+13x-13=2(x-5) equation: 


Simplifying
4x2 + 13x + -13 = 2(x + -5)

Reorder the terms:
-13 + 13x + 4x2 = 2(x + -5)

Reorder the terms:
-13 + 13x + 4x2 = 2(-5 + x)
-13 + 13x + 4x2 = (-5 * 2 + x * 2)
-13 + 13x + 4x2 = (-10 + 2x)

Solving
-13 + 13x + 4x2 = -10 + 2x

Solving for variable 'x'.

Reorder the terms:
-13 + 10 + 13x + -2x + 4x2 = -10 + 2x + 10 + -2x

Combine like terms: -13 + 10 = -3
-3 + 13x + -2x + 4x2 = -10 + 2x + 10 + -2x

Combine like terms: 13x + -2x = 11x
-3 + 11x + 4x2 = -10 + 2x + 10 + -2x

Reorder the terms:
-3 + 11x + 4x2 = -10 + 10 + 2x + -2x

Combine like terms: -10 + 10 = 0
-3 + 11x + 4x2 = 0 + 2x + -2x
-3 + 11x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + 11x + 4x2 = 0

Factor a trinomial.
(-3 + -1x)(1 + -4x) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-3, 0.25}

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