.5(2x+1)(2x-3)=2.5

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Solution for .5(2x+1)(2x-3)=2.5 equation:


Simplifying
0.5(2x + 1)(2x + -3) = 2.5

Reorder the terms:
0.5(1 + 2x)(2x + -3) = 2.5

Reorder the terms:
0.5(1 + 2x)(-3 + 2x) = 2.5

Multiply (1 + 2x) * (-3 + 2x)
0.5(1(-3 + 2x) + 2x * (-3 + 2x)) = 2.5
0.5((-3 * 1 + 2x * 1) + 2x * (-3 + 2x)) = 2.5
0.5((-3 + 2x) + 2x * (-3 + 2x)) = 2.5
0.5(-3 + 2x + (-3 * 2x + 2x * 2x)) = 2.5
0.5(-3 + 2x + (-6x + 4x2)) = 2.5

Combine like terms: 2x + -6x = -4x
0.5(-3 + -4x + 4x2) = 2.5
(-3 * 0.5 + -4x * 0.5 + 4x2 * 0.5) = 2.5
(-1.5 + -2x + 2x2) = 2.5

Solving
-1.5 + -2x + 2x2 = 2.5

Solving for variable 'x'.

Reorder the terms:
-1.5 + -2.5 + -2x + 2x2 = 2.5 + -2.5

Combine like terms: -1.5 + -2.5 = -4
-4 + -2x + 2x2 = 2.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
-4 + -2x + 2x2 = 0.0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -1x + x2) = 0.0

Factor a trinomial.
2((-1 + -1x)(2 + -1x)) = 0.0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-1, 2}

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