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Simplifying
(2x + -3)(4x + 5) + (2x + -3) = 0
Reorder the terms:
(-3 + 2x)(4x + 5) + (2x + -3) = 0
Reorder the terms:
(-3 + 2x)(5 + 4x) + (2x + -3) = 0
Multiply (-3 + 2x) * (5 + 4x)
(-3(5 + 4x) + 2x * (5 + 4x)) + (2x + -3) = 0
((5 * -3 + 4x * -3) + 2x * (5 + 4x)) + (2x + -3) = 0
((-15 + -12x) + 2x * (5 + 4x)) + (2x + -3) = 0
(-15 + -12x + (5 * 2x + 4x * 2x)) + (2x + -3) = 0
(-15 + -12x + (10x + 8x2)) + (2x + -3) = 0
Combine like terms: -12x + 10x = -2x
(-15 + -2x + 8x2) + (2x + -3) = 0
Reorder the terms:
-15 + -2x + 8x2 + (-3 + 2x) = 0
Remove parenthesis around (-3 + 2x)
-15 + -2x + 8x2 + -3 + 2x = 0
Reorder the terms:
-15 + -3 + -2x + 2x + 8x2 = 0
Combine like terms: -15 + -3 = -18
-18 + -2x + 2x + 8x2 = 0
Combine like terms: -2x + 2x = 0
-18 + 0 + 8x2 = 0
-18 + 8x2 = 0
Solving
-18 + 8x2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '18' to each side of the equation.
-18 + 18 + 8x2 = 0 + 18
Combine like terms: -18 + 18 = 0
0 + 8x2 = 0 + 18
8x2 = 0 + 18
Combine like terms: 0 + 18 = 18
8x2 = 18
Divide each side by '8'.
x2 = 2.25
Simplifying
x2 = 2.25
Take the square root of each side:
x = {-1.5, 1.5}
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