2(t-2)(t+5)=t+5(t-4)

Solution for 2(t-2)(t+5)=t+5(t-4) equation:

Simplifying
2(t + -2)(t + 5) = t + 5(t + -4)

Reorder the terms:
2(-2 + t)(t + 5) = t + 5(t + -4)

Reorder the terms:
2(-2 + t)(5 + t) = t + 5(t + -4)

Multiply (-2 + t) * (5 + t)
2(-2(5 + t) + t(5 + t)) = t + 5(t + -4)
2((5 * -2 + t * -2) + t(5 + t)) = t + 5(t + -4)
2((-10 + -2t) + t(5 + t)) = t + 5(t + -4)
2(-10 + -2t + (5 * t + t * t)) = t + 5(t + -4)
2(-10 + -2t + (5t + t2)) = t + 5(t + -4)

Combine like terms: -2t + 5t = 3t
2(-10 + 3t + t2) = t + 5(t + -4)
(-10 * 2 + 3t * 2 + t2 * 2) = t + 5(t + -4)
(-20 + 6t + 2t2) = t + 5(t + -4)

Reorder the terms:
-20 + 6t + 2t2 = t + 5(-4 + t)
-20 + 6t + 2t2 = t + (-4 * 5 + t * 5)
-20 + 6t + 2t2 = t + (-20 + 5t)

Reorder the terms:
-20 + 6t + 2t2 = -20 + t + 5t

Combine like terms: t + 5t = 6t
-20 + 6t + 2t2 = -20 + 6t

Add '20' to each side of the equation.
-20 + 6t + 20 + 2t2 = -20 + 20 + 6t

Reorder the terms:
-20 + 20 + 6t + 2t2 = -20 + 20 + 6t

Combine like terms: -20 + 20 = 0
0 + 6t + 2t2 = -20 + 20 + 6t
6t + 2t2 = -20 + 20 + 6t

Combine like terms: -20 + 20 = 0
6t + 2t2 = 0 + 6t
6t + 2t2 = 6t

Add '-6t' to each side of the equation.
6t + -6t + 2t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
0 + 2t2 = 6t + -6t
2t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
2t2 = 0

Solving
2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
t2 = 0

Simplifying
t2 = 0

Take the square root of each side:
t = {0}