(2x-3)(2x-3)+5(2x-3)+4=0

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Solution for (2x-3)(2x-3)+5(2x-3)+4=0 equation: 


Simplifying
(2x + -3)(2x + -3) + 5(2x + -3) + 4 = 0

Reorder the terms:
(-3 + 2x)(2x + -3) + 5(2x + -3) + 4 = 0

Reorder the terms:
(-3 + 2x)(-3 + 2x) + 5(2x + -3) + 4 = 0

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) + 5(2x + -3) + 4 = 0
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + 5(2x + -3) + 4 = 0
((9 + -6x) + 2x * (-3 + 2x)) + 5(2x + -3) + 4 = 0
(9 + -6x + (-3 * 2x + 2x * 2x)) + 5(2x + -3) + 4 = 0
(9 + -6x + (-6x + 4x2)) + 5(2x + -3) + 4 = 0

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) + 5(2x + -3) + 4 = 0

Reorder the terms:
9 + -12x + 4x2 + 5(-3 + 2x) + 4 = 0
9 + -12x + 4x2 + (-3 * 5 + 2x * 5) + 4 = 0
9 + -12x + 4x2 + (-15 + 10x) + 4 = 0

Reorder the terms:
9 + -15 + 4 + -12x + 10x + 4x2 = 0

Combine like terms: 9 + -15 = -6
-6 + 4 + -12x + 10x + 4x2 = 0

Combine like terms: -6 + 4 = -2
-2 + -12x + 10x + 4x2 = 0

Combine like terms: -12x + 10x = -2x
-2 + -2x + 4x2 = 0

Solving
-2 + -2x + 4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.5, 1}

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