(4x-4)(3x+2)=4

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Solution for (4x-4)(3x+2)=4 equation:


Simplifying
(4x + -4)(3x + 2) = 4

Reorder the terms:
(-4 + 4x)(3x + 2) = 4

Reorder the terms:
(-4 + 4x)(2 + 3x) = 4

Multiply (-4 + 4x) * (2 + 3x)
(-4(2 + 3x) + 4x * (2 + 3x)) = 4
((2 * -4 + 3x * -4) + 4x * (2 + 3x)) = 4
((-8 + -12x) + 4x * (2 + 3x)) = 4
(-8 + -12x + (2 * 4x + 3x * 4x)) = 4
(-8 + -12x + (8x + 12x2)) = 4

Combine like terms: -12x + 8x = -4x
(-8 + -4x + 12x2) = 4

Solving
-8 + -4x + 12x2 = 4

Solving for variable 'x'.

Reorder the terms:
-8 + -4 + -4x + 12x2 = 4 + -4

Combine like terms: -8 + -4 = -12
-12 + -4x + 12x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-12 + -4x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -1x + 3x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -3 + -1x + 3x2 = 0 Solving -3 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.3333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.3333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.3333333333x + x2 = 0 + 1 -0.3333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.3333333333x + x2 = 1 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 1 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 1 + 0.02777777779 Combine like terms: 1 + 0.02777777779 = 1.02777777779 0.02777777779 + -0.3333333333x + x2 = 1.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 1.02777777779 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.013793755 and -1.013793755.

Subproblem 1

x + -0.1666666667 = 1.013793755 Simplifying x + -0.1666666667 = 1.013793755 Reorder the terms: -0.1666666667 + x = 1.013793755 Solving -0.1666666667 + x = 1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 1.013793755 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.013793755 + 0.1666666667 x = 1.013793755 + 0.1666666667 Combine like terms: 1.013793755 + 0.1666666667 = 1.1804604217 x = 1.1804604217 Simplifying x = 1.1804604217

Subproblem 2

x + -0.1666666667 = -1.013793755 Simplifying x + -0.1666666667 = -1.013793755 Reorder the terms: -0.1666666667 + x = -1.013793755 Solving -0.1666666667 + x = -1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -1.013793755 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.013793755 + 0.1666666667 x = -1.013793755 + 0.1666666667 Combine like terms: -1.013793755 + 0.1666666667 = -0.8471270883 x = -0.8471270883 Simplifying x = -0.8471270883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1804604217, -0.8471270883}

Solution

x = {1.1804604217, -0.8471270883}

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