(2x-6)(x+7)=4x^2-20x+24

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Solution for (2x-6)(x+7)=4x^2-20x+24 equation: 


Simplifying
(2x + -6)(x + 7) = 4x2 + -20x + 24

Reorder the terms:
(-6 + 2x)(x + 7) = 4x2 + -20x + 24

Reorder the terms:
(-6 + 2x)(7 + x) = 4x2 + -20x + 24

Multiply (-6 + 2x) * (7 + x)
(-6(7 + x) + 2x * (7 + x)) = 4x2 + -20x + 24
((7 * -6 + x * -6) + 2x * (7 + x)) = 4x2 + -20x + 24
((-42 + -6x) + 2x * (7 + x)) = 4x2 + -20x + 24
(-42 + -6x + (7 * 2x + x * 2x)) = 4x2 + -20x + 24
(-42 + -6x + (14x + 2x2)) = 4x2 + -20x + 24

Combine like terms: -6x + 14x = 8x
(-42 + 8x + 2x2) = 4x2 + -20x + 24

Reorder the terms:
-42 + 8x + 2x2 = 24 + -20x + 4x2

Solving
-42 + 8x + 2x2 = 24 + -20x + 4x2

Solving for variable 'x'.

Reorder the terms:
-42 + -24 + 8x + 20x + 2x2 + -4x2 = 24 + -20x + 4x2 + -24 + 20x + -4x2

Combine like terms: -42 + -24 = -66
-66 + 8x + 20x + 2x2 + -4x2 = 24 + -20x + 4x2 + -24 + 20x + -4x2

Combine like terms: 8x + 20x = 28x
-66 + 28x + 2x2 + -4x2 = 24 + -20x + 4x2 + -24 + 20x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
-66 + 28x + -2x2 = 24 + -20x + 4x2 + -24 + 20x + -4x2

Reorder the terms:
-66 + 28x + -2x2 = 24 + -24 + -20x + 20x + 4x2 + -4x2

Combine like terms: 24 + -24 = 0
-66 + 28x + -2x2 = 0 + -20x + 20x + 4x2 + -4x2
-66 + 28x + -2x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
-66 + 28x + -2x2 = 0 + 4x2 + -4x2
-66 + 28x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-66 + 28x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + 14x + -1x2) = 0

Factor a trinomial.
2((-11 + x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + x)' equal to zero and attempt to solve:

Simplifying
-11 + x = 0

Solving
-11 + x = 0

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

Add '11' to each side of the equation.
-11 + 11 + x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x = 0 + 11
x = 0 + 11

Combine like terms: 0 + 11 = 11
x = 11

Simplifying
x = 11

Subproblem 2
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
Solution
x = {11, 3}

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